By Howard Fendrich, AP Football Writer

The NFL wants team executives ready to be schooled in the ins and outs of a new labor contract as early as Thursday.

Players are gathering in Washington so they’re ready to vote on an agreement in principle even sooner than that.

Yes, signs are strong that football’s four-month lockout might almost be over.

Lawyers for both sides were scheduled to meet with a court-appointed mediator in New York on Tuesday, when representatives of retired players were expected to participate, too, in an attempt to close a deal to resolve the NFL’s first work stoppage since 1987.

“Making progress,” NFL Players Association outside counsel Jeffrey Kessler said as he left a Manhattan law firm after 8½ hours of talks Monday. Kessler also represents locked-out NBA players.

Commissioner Roger Goodell and NFLPA head DeMaurice Smith spoke to each other on the telephone Monday and planned to stay in regular contact.

“Nobody cheers for you at Mile 25 of a marathon. You still have to cross the finish line,” NFLPA spokesman George Atallah said in Washington. “There still are things that can get you tripped up, and we’re going to push through.”

Owners are set to hold a special meeting in Atlanta on Thursday, when they could ratify a new agreement — if there is one. Executives from all 32 teams then would be briefed there Thursday and Friday on how the terms would affect league business, two people familiar with the plan told The Associated Press.

The people said the clubs were told Monday that topics would include the 2011 NFL calendar, rookie salary system and guidelines for player transactions. They spoke to the AP on condition of anonymity because the process is supposed to remain confidential.

Any tentative agreement also must be approved by the players, of course, including star quarterbacks Tom Brady, Peyton Manning and Drew Brees and the other plaintiffs in an antitrust suit against the league that is pending in federal court in Minnesota.

Members of the NFLPA executive committee and representatives of every team were heading to Washington by Wednesday, in preparation for possible decisions on re-establishing a union and signing off on a tentative pact with owners.

Atallah said the players would be gathering “with the hope they have something to look at, and with the hope we can move forward on this.”

Owners locked out players on March 12, when the old collective bargaining agreement expired, leaving the country’s most popular professional sports league in limbo. The sides are trying to forge a settlement in time to keep the preseason completely intact. The exhibition opener is supposed to be the Hall of Fame game between the St. Louis Rams and Chicago Bears on Aug. 7.

The regular-season opener is scheduled for Sept. 8, when the Super Bowl champion Green Bay Packers are to host the New Orleans Saints.

Philadelphia Eagles quarterback Michael Vick tweeted Monday: “Sound like we gonna be back to work so soon!!!”

One issue standing in the way of a resolution, according to a person from each side of the dispute and speaking to the AP on condition of anonymity: Players want owners to turn over $320 million in unpaid benefits from the 2010 season. Because there was no salary cap that season, the old collective bargaining agreement said NFL teams weren’t required to pay those benefits.

On a separate matter, one of those people, as well as a second person familiar with the negotiations, also told the AP that a proposal currently under consideration would set up nearly $1 billion over the next 10 years in additional benefits for retired players. That would include $620 million in pension increases, long-term care insurance and disability programs. Representatives of retired players complained to the court recently that they had been excluded from negotiations.

In Minnesota, players’ lawyers filed a motion Monday asking for a summary judgment that the lockout is illegal and that players are entitled to damages. The NFL, meanwhile, asked the court for a week’s extension to file their formal response to the lawsuit; the original deadline was Monday.