In the midst of their five-game losing streak this season, the Redskins talked to at least two National Football League teams about trading quarterback Joe Theismann, according to league sources.

One of the teams, the Los Angeles Rams, rejected the proposed trade outright. But the Detroit Lions went as far as offering a player, apparently a reserve, in return for Theismann. The Redskins then cut off the talks.

The discussions took place in early October, just before the league's trading deadline. The Rams were having quarterback problems, Lion starter Gary Danielson was injured and Theismann, who will become a free agent Feb. 1 unless the Redskins sign him to a new contract, was struggling with Coach Joe Gibbs' new offense.

But the Redskins defeated Chicago Oct. 11 for their first victory and decided to stay with Theismann.

"You talk to clubs constantly about different players all the time," Redskin General Manager Bobby Beathard said yesterday. "But we weren't interested in trading Joe."

League sources, however, say that Theismann was being shopped to see what he would bring the Redskins in an open market. If Washington had been offered a substantial return for him, including a first-round draft choice, then it would have seriously considered trading him, those sources say.

Said Theismann yesterday: "They told us at the beginning of the year that no one was untouchable, so it really doesn't surprise me that they tried to trade me. Hopefully, now I have proven to them that it would have been a mistake if the trade had happened."

Theismann finished strongly the last 11 weeks of the season, producing the second best season by a quarterback in team history, completing 293 of 496 passes for 3,568 yards and 19 touchdowns.

Although Redskins owner Jack Kent Cooke, Beathard and Gibbs have said they want to sign Theismann to a new contract, Beathard admitted that an impasse in the upcoming negotiations could lead to a trade.

"I think a new contract can be worked out," Beathard said. "But we were a long way apart in terms of money when we talked in the spring. If a large gap remains after we negotiate for a while, everyone might want to go another route.

"But that's way down the road. We want to start talking in mid-January with Joe and his representative. We are going to make every attempt we can to sign him. It's going to be a tough negotiation, I'm sure."

As a free agent, Theismann, who earns $225,000 a year, would have the right to negotiate with other teams. But the Redskins either could match another contract offer or would be entitled to two first-round picks as compensation under terms of the current contract between the league and the NFL Players Association.

A trade could be consummated only if Theismann and the new team could agree to a contract, which gives the veteran quarterback considerable leverage. It also is doubtful that the Redskins would trade Theismann now unless they could obtain a first-string quarterback in exchange. Rookie Tom Flick is the only other quarterback on the active roster.

Baltimore's Bert Jones has been offered recently in trades, but the Redskins have shown no interest.

Neither side is discussing contract terms, but the Redskins are unlikely to pay more than $400,000 a year for Theismann. Theismann, however, has been expected to ask for well over $500,000 a season. Only six NFL quarterbacks were earning at least $300,000 in 1980, the last year for which league salary figures are available. Bob Griese, who retired before the current season, was the highest paid, earning $400,025 annually.

Theismann yesterday said the $500,000 figure "is out of line. My agent and I haven't sat down and discussed final demands yet. But my original proposal (in the spring) would not have put me among the top five quarterbacks in the league."

Also, it now appears that veteran cornerback Lemar Parrish could be involved in a trade, especially if the Redskins draft some young cornerbacks.

Parrish was bothered by a bad knee much of the 1981 season and played behind Jeris White the last month. Parrish still has ability, however, and the Redskins, who have tired of his contract demands, probably will see what draft choices he might bring.

Team sources also wouldn't rule out fullback John Riggins being involved in a deal. But first the Redskins and Riggins are waiting for a decision from arbitrator Bert Luskin over the grievance he filed last year against Washington following his surprise retirement from football. Luskin's decision is expected soon.

Riggins has veto power over a trade. And, depending on the arbitrator's ruling, he will either be in the option year of his $300,000 contract or he will be a free agent. That means Washington or another team would have to sign him to a new, expensive contract.

Last spring, Beathard admitted talking to at least five teams about Riggins, including Miami, Houston and San Diego. But nothing serious developed.

Other veteran Redskins who have trade value include defensive tackle Dave Butz, linebacker Brad Dusek and kicker Mark Moseley. But Gibbs has said he would be very reluctant to trade any of his best players.

The Redskins also have to decide how many of 14 other potential free agents they want to sign to new contracts in the offseason.

Thirteen will be free agents Feb. 1: Butz, punter Mike Connell, halfback Wilbur Jackson, cornerback Joe Lavender, receiver Terry Metcalf, fullback Ricky Claitt, tight end Rich Caster, Dusek, linebacker Pete Cronan, tight end Bob Raba, center Bob Kuziel, center Dan Peiffer and defensive end Karl Lorch. Cornerback Ray Waddy is entering the option year of his contract.

Kuziel, who has a chronic back injury, has retired after being advised by doctors to not play football again. Peiffer spent the season on injured reserve and most likely will be released. Lorch, who was benched for the last six games, also probably won't be re-signed. Caster may retire.

His teammates have selected Joe Washington as the team's most valuable player this season . . . Beathard said the Redskins want to draft a "pass rushing" defensive lineman and a "speed burner" wide receiver with size who would complement veteran Art Monk.