In another very hopeful sign for the NFL’s labor dispute, sources confirmed to The Post that league commissioner Roger Goodell and union chief DeMaurice Smith met for a private dinner lasting nearly two hours Wednesday night at a Midtown restaurant.

The secret and highly unusual sit-down came at Patroon just hours after the two leaders were involved in another round of closed-door talks between negotiating parties on Long Island.

Those talks, combined with what a witness said was “a very jovial dinner” between Goodell and Smith, are prompting optimism that the league’s three-month labor dispute could soon end before any games or training-camp time are lost.

A league spokesman declined comment on the private dinner. The decertified union did not respond to messages.