The Washington Post’s Mark Maske reports that the NFL could finalize its new Collective Bargaining Agreement within the next 2-3 weeks.

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.

Rotoworld.com notes that Maske “has been one of the most plugged-in and reliable reporters on the CBA talks,” so that’s comforting. And after speaking with Vikings defensive end Jared Allen and former Titan Kevin Carter over the last two weeks, I too get the sense that the two sides are getting closer.

That said, both Allen and Carter expressed that there is still a lot that needs to be ironed out. The players are holding their ground when it comes to benefits for both current and former athletes. That’s a huge sticking point for them, as they want to ensure that the league will take care of retired players long past their days in pads and cleats.

But at the very least, it appears as though these labor talks are moving in the right direction. It’s a very good sign that the two sides are talking out of court.