Full negotiating teams for the NFL and locked out players reconvened Wednesday in New York to try to apply the elusive finishing touches to a deal to end the sport’s shutdown. People in the sport said it appeared an agreement in principle between the two sides was close and estimated it was likely to be completed between Friday and next Tuesday, barring further complications.

Each side issued a written statement early Wednesday saying the time for a resolution to the four-month-old lockout had arrived.

Quarterbacks Tom Brady, Peyton Manning and Drew Brees said in a statement issued by the NFL Players Association: “We believe the overall proposal made by the players is fair for both sides and it is time to get this deal done.” The three standout quarterbacks are among the named plaintiffs in the players’antitrust lawsuit against team owners.

“This is the time of year we as players turn our attention to the game on the field,” the quarterbacks’ statement continued. “We hope the owners feel the same way.”

The league responded by issuing a statement that said: “We share the view that now is the time to reach an agreement so we can all get back to football and a full 2011 season. We are working hard with the players’ negotiating team every day to complete an agreement as soon as possible.”

Several people not involved in the negotiations but familiar with them said they did not expect a handshake deal to be completed Wednesday. But they said an an agreement in principle was possible in coming days.

By some estimates, a pact is possible by Friday. But the two sides have been within striking distance of an agreement for several weeks, and previously have suffered negotiating setbacks that kept them from reaching an accord.

Other people, speaking on the condition of anonymity because the deliberations are at a sensitive stage, said a deal might not come until Tuesday. That’s when deadline pressure will increase and could force the two sides into a compromise, because both sides are scheduled to meet Tuesday in Minneapolis with their court-appointed mediator, Chief Magistrate Judge Arthur J. Boylan, those people said.

Boylan is not attending this week’s negotiating sessions but is said to be available to consult via phone or other means.

Attorneys and staff members for the league and players met Monday and Tuesday in New York and appeared to make progress toward readying a written document for completion if the remaining issues are settled.

Talks between the full negotiating teams broke off temporarily last Friday after they stalled over the details of a rookie pay system. The league wants to curb the amount of guaranteed money in the contracts of rookies selected in the first round of the NFL draft. The players side appears willing to agree to some provisions, but has been resisting a system as restrictive as the one the league is seeking.

Other issues remain unsettled. They may include rules for free agency and ongoing court oversight of the agreement, according to people familiar with the talks. But it was not clear if disagreement over any of those issues could cause the talks to unravel if negotiators are able to work out the particulars of a rookie compensation system.

The two sides also appear close to an accord on the core economic issue of how to divide the sport’s revenue, currently pegged at $9.3 billion annually. The deal will include a include a salary cap system that will give the players just less than half the revenue, people familiar with the bargaining have said.

The owners are scheduled to meet July 21 at an airport hotel in the Atlanta area. If a deal is reached before then, the owners could take a ratification vote that day. An agreement must be approved by at least 24 of the 32 owners and separately by the players.

If the talks stall again, the owners could use that meeting to consider canceling preseason games. The preseason opener, the Hall of Fame Game, is scheduled for Aug. 7 in Canton, Ohio, between the Chicago Bears and St. Louis Rams. That game could be in jeopardy even if a deal is struck in coming days, but the rest of the preseason likely would be preserved. The regular season is scheduled to begin Sept. 8.

Players have been locked out by the owners since March 12. A federal appeals court ruled last Friday that the lockout could continue. Another court ruling, on possible damages in a case involving the sport’s television contracts, is still pending. The players are seeking about $2.5 billion in punitive and compensatory damages, and want U.S. District Judge David S. Doty to bar owners from receiving approximately $4 billion in annual TV revenue if the lockout extends into the regular season.