The NFL and locked out players have made enough progress in their recent negotiations that a deal between the two sides is within reach during the next two or three weeks, people on both sides of the dispute said Tuesday.

Owners of the 32 teams, scheduled to attend a meeting in Chicago Tuesday, have been told to leave their schedules open in case the session runs late that night 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.

It is possible--but very unlikely--that the owners could vote on a labor deal at that meeting, said several of the people, who did not participate in the talks but are familiar with developments. It is more likely, they said, that owners could give negotiators their opinions and a deal with the players could be completed the following week.

A deal that week, just before the July 4 holiday, appears increasingly realistic, said people on both sides of the dispute.

Others, however, cautioned that a deal between league and the players remains less than a certainty and talks still could unravel.

Talks between the league and the players are continuing. NFL Commissioner Roger Goodell and DeMaurice Smith, executive director of the dissolved players’ union, participated in mediated negotiations in each of the previous two weeks, along with small groups of owners and players. The talks were held in New York last week and in Chicago the previous week.

The talks resumed Tuesday in Maryland, and a meeting was also scheduled for Wednesday. People from both sides who are following them closely said the progress made this week will determine what happens at next week’s owners meeting. Any deal would have to be approved by at least 24 of the 32 owners.

It also appears that the dialogue between the two sides is taking place via informal talks between the formal negotiating meetings.

It is considered unlikely that this week’s talks would produce a tentative deal for the owners to vote on next week.

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