The Italian champions are heading for their seventh consecutive Scudetto triumph, after Napoli's draw against Torino on Sunday.
Allegri, who has another two years left on his contract, is one of several big names to replace Arsene Wenger who leaves the Gunners after their final game at Huddersfield Town on Sunday.
According to Sky Sports News, once his fourth-straight title with the Turin giants is in the bag, the 50-year-old will sit down with the club hierarchy to thrash out his future.
He will meet with chairman Andrea Agnelli and CEO Guiseppe Marotta.
The Italian champions are keen for Allegri to extend his stay, but will not stand in his way if he decides he wants to leave.
However, there have been reports Allegri and other frontrunner Luis Enqriue are concerned about working under the new management structure in North London.
The former Barcelona manager is ready to return to the game after taking a year off following his departure from the Nou Camp last summer.