DeMaurice Smith, right, the executive director of the dissolved players’ union, has taken part in the recent labor talks along with NFL Commissioner Roger Goodell, along with small groups of owners and players. (Hannah Foslien/GETTY IMAGES)

The NFL’s labor talks resumed Tuesday amid signs that enough progress has been made in recent negotiations that a deal is within reach in the next two to three weeks, according to people on both sides of the dispute.

Owners of the 32 teams have been told to leave their schedules open in case a meeting scheduled for next Tuesday in Chicago runs late or spills over into the following day, said several people who spoke on the condition of anonymity because the deliberations are at a sensitive stage. Several people in the sport left open a small chance of a deal being completed within days.

It is possible, but unlikely, that owners would vote on a labor deal at their meeting, people familiar with the negotiations said. It is far more likely, they said, that the owners would review possible terms with their negotiators and a deal with locked-out players could be completed the following week.

Any deal with the players would have to be approved by at least 24 of the 32 owners.

An accord just before the July 4 holiday appears increasingly realistic, said people on both sides of the talks who did not participate but have knowledge of them.

The recent negotiations have been marked by a dramatic change in tone, people throughout the sport have said, perhaps because courtroom decisions that favor the owners have affected negotiating leverage and the threat of a shortened season looms if the talks stall again.

Despite caution that the talks still could unravel, the prevailing sentiment among those with knowledge of the negotiations is that the deal is likely to get done and the main question at this point is when.

Indianapolis Colts owner Jim Irsay said last month that a deal would have to be completed by July 4 to allow time for a free agent signing period followed by a full training camp, preseason and regular season.

Irsay wrote Tuesday on Twitter that he hopes the two sides “keep making progress, have a full training camp and season, put this stuff [to] bed.”

Others, however, said the issues are very complex and even if progress continues, it might take a week or two longer than the current early-July target for the deal to be finished.

George Atallah, assistant executive director of external affairs for the NFL Players Association, wrote Tuesday on Twitter: “Just like I don’t predict about how Federal Judges will rule on cases, I don’t predict when a resolution to the lockout will come.”

Washington Redskins defensive tackle Lorenzo Alexander said: “Until they actually get something agreed upon, signed and across the table, then I’m not even putting much weight into anything. I’ll wait and see when something’s done and then I’ll be happy.”

The league and players have been at odds over how to divide more than $9 billion in annual revenue. In a previous round of talks, the two sides were about $320 million apart on the salary cap in the first year of a deal and had not reached an accord on how to divide future revenue that exceeds projections.

The league is seeking to avoid ongoing court oversight of the sport’s labor pact and has proposed blood-testing players for use of human growth hormone. The NFL previously agreed not to immediately implement a proposed 18-game regular season and offered the players reductions in offseason workouts. The two sides also must agree to a rookie pay system.

Players have been locked out by owners since March 12, the day after they dissolved their union and filed an antitrust lawsuit against the NFL. The regular season is scheduled to begin Sept. 8.

The talks that resumed Tuesday on Maryland’s Eastern Shore were scheduled to continue through Wednesday. Attorneys for both sides rejoined the talks Tuesday after they were left out of negotiations the previous two weeks.

NFL Commissioner Roger Goodell and DeMaurice Smith, the executive director of the dissolved players’ union, have participated in the recent talks, along with small groups of owners and players. The talks were held on Long Island last week and in suburban Chicago the previous week.

Dialogue between the two sides also is taking place via informal talks between formal negotiating sessions.

The league and players are awaiting a ruling by a federal appellate court on the legality of the lockout. A federal court ruling that ordered an end to the shutdown was put on hold by the same appeals court.

Staff writer Mike Jones contributed to this report.