NFL commissioner Roger Goodell, left, and DeMaurice Smith, executive director of the former NFLPA, are running out of time to get their sides to come to a compromise before preseason games must be cancelled. (Brian Blanco/Associated Press)

Representatives of the NFL and locked-out players are scheduled to resume face-to-face negotiations Tuesday in New York with time running short for them to complete a deal to ensure a substantial free agent signing period before on-time training camps and a full preseason.

The two sides remained in contact via telephone and electronic communications over the holiday weekend after meeting last week in Minneapolis under the supervision of their court-ordered mediator, Chief Magistrate Judge Arthur J. Boylan. Negotiators for the league and the players had a relatively brief meeting Friday after a long day of talks Thursday.

The talks nearly broke down around midday Thursday, but the two sides stayed at it and appeared to repair the rift while meeting into early Friday morning.

That seemed to get the league and the players back within striking distance of a deal, with hopes that an agreement could be completed as soon as late this week. Talks are scheduled through Friday. NFL Commissioner Roger Goodell and DeMaurice Smith, the executive director of the NFL Players Association, are to participate. They are to be joined by staff members Tuesday and Wednesday. Groups of owners and players are scheduled to rejoin the talks Thursday and Friday.

On Monday, the group of retired players involved in the antitrust lawsuit against the NFL’s team owners filed a complaint in federal court in the Minneapolis area, asserting that the league and players are violating antitrust laws by negotiating possible settlement terms.

It was not immediately clear what effect, if any, the retired players’ complaint will have on the negotiations between the league and the current players.

A handshake deal by the end of this week would enable the sport to have a free agent signing period of a significant length before teams would open their training camps in late July to early August, and a full preseason would be played beginning next month. Hundreds of players potentially eligible for free agency have been in limbo since the lockout began March 12. Free agent signings and trades of players have been prohibited during the lockout.

The league apparently does not intend to allow free agency to begin until a new collective bargaining agreement is written and formally approved. People familiar with the process previously have said it is likely to take about two weeks to turn a handshake deal into an official, written agreement. So a handshake deal by Friday might result in free agency commencing around July 22, under that timetable.

It is possible, however, that the turnaround time from handshake deal to formal agreement potentially could be condensed to less than two weeks, which might allow the sport to have free agency and on-time training camps even if a tentative deal does not come until closer to July 15. Greg Aiello, the NFL’s senior vice president of public relations, wrote on Twitter over the weekend that “lawyers are drafting language for [a] potential agreement, sharing it with” the players’ side.

That did not mean there was an agreement already in place, Aiello wrote. But the work already being done on crafting the language for a potential written agreement could lead to a quicker turnaround from a handshake deal to a formal document. Aiello wrote on Twitter that the “lawyers have been drafting potential CBA language for a while.”

Last week’s tumultuous negotiations underscored what many people within the sport have been saying for weeks: that a deal is within reach but the talks are precarious and still can unravel.

The negotiations appeared on the verge of breaking off last Thursday over continued disagreements about the central economic issue of the dispute: how the two sides will divide the sport’s approximately $9.3 billion in annual revenues.

The talks were mended during the late-night talks last Thursday and early Friday. Even so, people not involved in the negotiations but familiar with them said over the weekend that significant negotiating challenges remain and that although there has been progress, much more is needed.

Owners are wary that preseason games might have to be canceled if there’s no deal soon, people familiar with the talks said. Officials have said the preseason generates about $200 million per week in league-wide revenues. It appears there have been recent negotiating tensions over issues such as a rookie pay system and retiree benefits in addition to the central division-of-revenues issue.