The National Football League Players Association will offer a written counterproposal to the NFL Management Council Tuesday, with two days of negotiations in suburban Virginia having yielded no substantial progress toward averting a players strike next week, according to the top negotiators on each side.

The key issue of free agency still had not been discussed after five hours of negotiations Saturday and 6 1/2 hours yesterday at the Dulles Ramada Renaissance Hotel.

Negotiations were recessed in early evening, and both sides indicated they will resume Tuesday afternoon in the Washington area. Staff experts are expected to meet today to discuss insurance, severance and pension issues.

The NFLPA has announced a Sept. 22 strike date unless it reaches accord on a collective bargaining agreement to replace the one that expired Aug. 31.

Gene Upshaw, executive director of the Players Association, said that the two weekend days of discussion produced "no areas in which we made an agreement or came close to an agreement . . . I don't think we made any progress."

Upshaw said the union, in response to a management offer made last Monday, "will present a counterproposal which we feel will go a long way toward a settlement."

Jack Donlan, executive director of the Management Council, had been seeking a written counterproposal from the union all weekend. But he said he did not consider it a sign of progress. "You have to wait and see what that counterproposal is," he said.

Donlan characterized the Saturday and Sunday talks as "the type of discussions we should have had months and months ago." Donlan continually has said the union has not wanted to negotiate and has too many issues on the table. Upshaw has denied both assertions.

Donlan reiterated that the owners will not yield their position on opposing unrestricted free agency, a major demand by the players.

"We're not going to give them free agency so there is a lot of bidding among clubs," he said. "We've made that clear from the beginning. We're not trying to hide anything there. The system has worked well . . . We recognize what it's done for baseball. We don't want to do that."

Asked if there were a middle ground on the issue of free agency, Upshaw said, "They seem to think there's no middle ground on anything. They think their position is the middle ground."

Nevertheless, Upshaw said it was still possible to avert a strike. He added: "If they remain so bull-headed, maybe there is no middle ground. Maybe we will have to strike."

Donlan said discussions about free agency occurred indirectly this weekend, but were not discussed as a single issue in the formal talks.

The Management Council proposal on free agency keeps the basic framework of compensation and right of first refusal.

Meanwhile, in eight of 13 NFL stadiums around the country, including RFK in Washington, many players exchanged solidarity handshakes at midfield, drawing some boos from fans in Washington and Green Bay.