The NFL and representatives of its locked-out players exchanged letters Thursday in which each side proposed terms for the resumption of talks aimed at ending the sport’s nearly four-week-old shutdown. But there was little optimism that the two sides would renew negotiations.

The league proposed a return to talks overseen by federal mediator George H. Cohen, assuring players they would not compromise any legal position by participating. The players asked the league to participate in negotiations to settle their antitrust lawsuit against the NFL under the auspices of a federal court in Minnesota.

Sources on both sides of the dispute said neither side was interested in the other’s conditions for renewed talks.

The correspondence came one day after a federal judge in St. Paul, Minn., urged the parties to resume talks using the resources of her court. U.S. District Judge Susan Richard Nelson also told the two sides at the conclusion of a hearing Wednesday that she would need “a couple of weeks” to rule on the players’ request to end the lockout imposed by owners March 12.

Talks between the league and players have been on hold since the negotiations with Cohen collapsed March 11. The players dissolved their labor union, the NFL Players Association, that day and filed an antitrust lawsuit against the sport’s franchise owners.

League officials have said since that they do not consider the players’ decertification of their union valid and would participate in further talks only via collective bargaining with a reconstituted union.

Players and their allies said the decertification was valid and they would not re-form the union to resume collective bargaining. Talks could take place only in the form of discussions between the league and the players’ attorneys to settle the lawsuit, they said.

In its letter to the league Thursday, a copy of which was filed with Nelson’s court, the players’ side said it was willing to accept Nelson’s offer for talks mediated by the federal court in Minnesota. A source on the players’ side said its offer was for negotiations to settle their lawsuit, not collective bargaining.

The NFLPA, now technically a trade association, issued a written statement that said: “Though the injunction to lift the owners’ lockout remains under Judge Nelson’s consideration, the players took to heart her advice given during Wednesday’s hearing that the two sides should not delay to meet. The players expressed their hope that mediation under court oversight will begin immediately.”

An NFL source said the league remained uninterested in lawsuit settlement negotiations.

The league, in its letter to the players’ side Thursday, urged a resumption of the talks overseen by Cohen, the director of the Washington-based Federal Mediation and Conciliation Service. Greg Aiello, the NFL’s senior vice president of public relations, said in a written statement the league’s letter promised owners would participate in the negotiations and the goal would be to resolve all outstanding issues between the parties.

According to Aiello, the league’s letter said players would be assured they wouldn’t compromise any legal position by participating in talks mediated by Cohen.

But the players’ side believes talks with Cohen would be unproductive since the previous round of talks with him did not yield a settlement, a source said. The sourced added that the players are wary of the league’s motives. The players thought Wednesday’s hearing went well for them.

Nelson did not say during Wednesday’s hearing how she would rule on the players’ request for an injunction to end the lockout.

Any ruling by Nelson could be appealed to the U.S. Court of Appeals for the Eighth Circuit.