Efforts to end the 23-day-old strike by National Football League players remained stalemated last night after management rejected two offers by the union that would have returned the players to work without a collective bargaining agreement.

The second rejection followed an offer by union head Gene Upshaw to modify the union's proposal, made Monday, for binding arbitration if mediation failed. Upshaw said the union was willing to remove the critical issue of players' free agency from the proposed arbitration, while still using that process to resolve other issues preventing a settlement.

"We have rejected binding arbitration on any and all issues," said Jack Donlan, executive director of the owners' Management Council, in New York a few minutes after Upshaw held a news conference in Washington announcing the union's latest bid to return to work.

Now, the solidarity of the union faces another crucial test today because management has set a 1 p.m. deadline for players to report to practice and be eligible to be paid for this week's games. If the players remain solid -- and their union officials said they would -- then more economic pressure switches to the owners. If replacement players play a third game this week, they qualify for such benefits as playoff money, severance and pension.

The Washington Redskins voted unanimously last night to stay on strike, according to player representative Neal Olkewicz. Defensive end Dexter Manley, who did not attend the meeting of about 50 players, said earlier in the day he planned to return to work this morning. Two weeks ago, he said he was considering going back, then changed his mind.

Striking players on at least five other teams -- the Dallas Cowboys, Los Angeles Rams, Cincinnati Bengals, Atlanta Falcons and Kansas City Chiefs -- also had voted by late last night to remain out. But four more individual union members -- three Pittsburgh Steelers and one from the Los Angeles Raiders -- crossed picket lines yesterday, meaning about 135 of the 1,585 players represented by the NFL Players Association have reported back.

Also yesterday, the Chicago Bears traded regular reserve quarterback Doug Flutie to the New England Patriots. His agent, Boston attorney Bob Woolf, said the 1984 Heisman Trophy winner, who has been in the strikers' ranks, would play Sunday. New England Coach Raymond Berry announced that Flutie would start for the Patriots' replacement team.

"They're bent on busting the union," Upshaw said after the owners rejected the NFLPA's second offer. "What we have out there now is really a threat on the part of management to see if the players will break ranks. It just shows the people in control there at the NFL don't want to reach an agreement. It doesn't matter how many times we try. They just refuse at every turn."

Upshaw said he and Donlan had spoken twice by telephone yesterday and expected to be in touch with each other last night. He characterized the tone of those conversations as being starkly contrasting to the public statements being released by the Management Council.

What Upshaw and Donlan were discussing yesterday were not the 30 or so unresolved issues on the bargaining table, but five issues that would get the players back to work in time for Sunday's games.

Upshaw said the two sides agreed on not disciplining players for strike activities and guaranteeing the playing contracts of union officers, player representatives and their assistants for the rest of the season.

But there was disagreement on three issues, two of which Doug Allen, Upshaw's top aide, called "an insurmountable problem." The third issue was the owners refusing to freeze the rosters for the season; instead they offered a two-game salary guarantee, meaning if a player returned to work, he could be cut immediately, and would be paid two weeks' salary.

The union was sure there was more compromise possible on that issue. Allen's "insurmountable problem" had to do with the interlocking issues of binding arbitration on the unresolved economic items and extending the terms of the 1982 collective bargaining agreement until a new agreement is reached.

Upshaw said such a proposal would mean the 1982 agreement would be in effect "in perpetuity . . . forever," indicating that there would be no need for the owners ever to reach a new contract.

"There has to be an end point at which you get a new agreement," Allen said. "If we made this deal in '74, we'd still have the terms of the '74 deal in which the minimum salary is $12,000, there was no severance and the pension was about one-sixth of what it is today. You can go down the whole list."

Allen said the only way to guarantee a conclusion to the negotiations is through arbitration.

Donlan agreed that the central problem was binding arbitration, which would follow six weeks of mediation. Under binding arbitration, the two sides would agree to have a mutually acceptable third party hear the contrasting arguments and decide the issues. Under mediation, the third party would act to facilitate a settlement, but would not have the power to decide individual issues.

"We're not going to arbitrate our system, as you know it, away," Donlan said. "We don't want an outsider to tell us what to do . . . I've talked with Gene about this before and I told him I reject this. Why go public, then, if he knew we'd reject this?"

He said he told Upshaw the owners would not accept binding arbitration, then added, "Gene said, 'What if we have mediation on {free agency} and everything else could go to binding arbitration {if unresolved}?' "

Donlan said he answered, "We're not going to arbitrate {free agency} or the length of the contract, or the pension issue or any of the control issues out there."

The owners on the Management Council's six-member executive committee were as adamant about rejecting binding arbitration as they had been in rejecting any efforts to change the foundation of the free agency system, by eliminating either compensation or right of first refusal.

"I don't think anybody is favorably inclined to hand the future of our business to an arbitrator," said Dallas Cowboys President Tex Schramm, a hard-liner in this strike. "This should be resolved through negotiations. I don't think the NFL has been in business 65 years to have its future based on the finding of someone not in the business."

Added Miami Dolphins owner Joe Robbie: "Arbitrators sometimes go way beyond the issues that are handed to them."

While Upshaw said he was seeking alternatives to get the players back to work, Donlan said he saw no reason for resuming negotiations at this time.

"No, no, no. I don't see that at all," he said in reply to a question. "The reason we left Tysons Corner {Sunday afternoon} is that we went round and round and round and weren't closing in on anything."

Donlan and Upshaw had negotiated in suburban Virginia for six days, agreeing on eight minor issues, only two different from 1982 language, among 38 articles in the collective bargaining agreement.

That led to a meeting of the player representatives of the 28 teams outside Chicago Monday, at which time they agreed to the back-to-work proposal that was rejected by the Management Council yesterday, the counterpropsal that the players rejected, and then the owners rejection of the players' second offer.

Meanwhile, all three television networks said they would continue to televise replacement games this week even though ratings again dipped for the second straight week of replacement games.

Television ratings for ABC's "Monday Night Football" declined slightly. The Denver Broncos-Los Angeles Raiders game -- which drew a replacement-high 61,230 fans to Denver's Mile High Stadium -- received a national Nielsen rating of 12.9. Last week's Monday night game between the San Francisco 49ers and New York Giants game received a 13.8 rating.

The first two Monday night telecasts of the season, which took place before the players went on strike, averaged a 20.9 rating.

The rating represents the percentage of the nation's 88.6 million television households watching a program. The Sunday games on CBS and NBC were down 10 percent last week after dropping 29 percent the first two weeks.

Some players were finding it difficult to understand the latest move by the owners.

"It's confusing," Dallas player representative Doug Cosbie said. "Now we are bargaining just to get closer to bargaining on a contract. We felt there was a good chance we would be able to go back to work. But now it looks like we will still be out this week."

In Los Angeles, where 10 Rams have crossed the picket lines, most of the team's 46 strikers attended a 90-minute meeting after which guard Tom Newberry said, "We're supporting the union. Whatever the union recommends, we'll do."

One Ram who didn't attend the meeting was star running back Eric Dickerson. But Gary Jeter, the team's assistant player representative said, "We've spoken to Eric. He says he's not going back in until the offensive line crosses."

In Cleveland, player representative Mike Pagel conceded that the Browns were becoming increasingly restless. "If you were losing the money these guys are, you'd be restless, too," Pagel said.