Executive Director DeMaurice Smith and the NFL Players Association may be close to reaching a deal with league owners. (Richard Drew/AP)

A virtually completed deal to end the NFL’s four-month lockout is expected to be presented to player representatives on Wednesday for review and possible recommendation of approval, several people familiar with the deliberations said Tuesday night.

Attorneys for the league and players met Tuesday in New York with their court-appointed mediator, Chief Magistrate Judge Arthur J. Boylan, and failed to resolve all the remaining issues, according to people not involved in the negotiations but familiar with them. But the two sides made sufficient progress that they intended to have a draft ready for presentation to the players Wednesday in Washington, those people said, speaking on the condition of anonymity because of the sensitivity of the deliberations.

Members of the ruling executive committee of the NFL Players Association met Tuesday in Washington. They are to be joined Wednesday by team player representatives. After Wednesday’s review, that group could recommend approval of the deal to all NFL players. The agreement would have to be approved by a majority of the close to 2,000 players, and their vote could come by conference call or e-mail as soon as late Wednesday. The players could take a single vote to approve the deal and re-form their union, which they dissolved in March.

The owners are scheduled to meet Thursday in Atlanta and could take an approval vote then. The agreement would have to be ratified by at least 24 of the 32 owners.

Michael Hausfeld, an attorney for the retired players involved in the antitrust lawsuit against the league, said after participating in Tuesday’s meeting in New York that he believed a deal between the current players and the league was imminent.

“I think it will happen in the even nearer future than you think,” Hausfeld said in a telephone interview early Tuesday evening.

Hausfeld said the issues involving the retired players would be resolved later and “we made it clear that the retiree issues are not an impediment to a resolution” between the current players and the league.

The players will be presented with hundreds of pages of legal documents but people within the sport said their review of the proposed deal will be based largely on the summary provided by DeMaurice Smith, the executive director of the NFL Players Association.

NFL officials have said the lockout, which began March 12, will be lifted only when there is an official, signed collective bargaining agreement. If both sides approve the deal this week, free agency could begin by early next week. Teams likely will be given a three-day window to try to re-sign their own free agents before those players are allowed to sign elsewhere.

It appeared late Tuesday that most of the players who are among the named plaintiffs in the players’ antitrust lawsuit against the owners were on board with a proposed settlement, though no resolution had been reached.

Yahoo Sports reported that two of the named plaintiffs in the lawsuit, San Diego Chargers wide receiver Vincent Jackson and New England Patriots guard Logan Mankins, were seeking specific concessions as part of a settlement. According to the report, Mankins and Jackson wanted to be declared unrestricted free agents or compensated with $10 million each. Each player was named his team’s franchise player earlier this year after being involved in a contract dispute last year arising from the terms of a season without a salary cap.

The players’ side also wanted the restoration of $320 million in lost benefits for all the players stemming from the uncapped year, according to people within the sport.

It did not appear Tuesday that the league was inclined to make significant concessions in either area, given that the terms of the uncapped year were collectively bargained with the players as part of the sport’s previous labor deal.

There also was continuing talk within the sport that the players’ side wants to restrict teams’ use of the franchise-player tag multiple times on the same player, potentially making quarterbacks Peyton Manning and Drew Brees free agents at some point. Manning and Brees also are among the named plaintiffs in the antitrust lawsuit.

Manning was named the Colts’ franchise player earlier this year, but it’s not clear if the effort on his behalf would be for him to be a free agent immediately or following the upcoming season. Brees has one season remaining on his contract with the Saints.

A spokesman for the NFL Players Association suggested earlier Tuesday that some of the latest reports might be inaccurate.

“If you’re a player and you’re reading some of the media reports today, read all of them with skepticism,” George Atallah, the Players Association’s assistant executive director of external affairs, wrote on Twitter.

Minnesota Vikings punter Chris Kluwe was critical of Brees, Manning, Mankins and Jackson, writing on Twitter that “once again greed is the operative byword.”

Brees wrote Tuesday night on Twitter, “I hesitate to even dignify the false media reports with a response, but obviously they are leading people astray.”

Brees also wrote: “I want no special perks. My job is to get a fair deal for all players, and I am proud to represent them all — past, present and future.”

Jackson also took to Twitter, writing that he had made “no demands.”

A signed deal could be worth an estimated $50 billion or more to all NFL players over 10 seasons.

Hausfeld said accounts of the league and current players agreeing to close to $1 billion in improvements in retiree benefits over 10 years were inaccurate but that the two sides had agreed to a $620 million “legacy fund” for retired players over the duration of the deal.The requirement for players with expired contracts to be eligible for unrestricted free agency is to be restored to four seasons, after being raised temporarily to six seasons in the uncapped year. The 18-game season once proposed by the owners has been shelved, at least for now. The league proposed having players blood-tested for human growth hormone.

People within the sport declined Tuesday night to call it an agreement in principle because of the remaining unresolved issues. But that might have been a matter of semantics, given that the major issues of the dispute have been resolved. The proposed deal is to be for 10 years and is to give the players just less than half the sport’s revenues, about 46.5 to 48 percent, under a salary cap system. This season’s salary cap is to be set at approximately $141 million per team for players’ salaries and benefits, of which about $120 million would go to players’ salaries. The proposed deal contains a rookie pay system.

Since late last week, the two sides had discussed potential reductions in offseason workouts for players and reduced hitting in some practices during training camp and the season.