Van Gaal is under pressure at Man United following some increasingly meek attacking displays from his side.
There have been reports this week that Pep Guardiola is interested in taking over at the club but United have also identified Allegri as a target.
Allegri guided Juventus to the Champions League final last season as well as winning Serie A but the team have struggled this time around, with the Old Lady currently sitting fifth in the league.
Van Gaal and Allegri’s contracts at United and Juventus, respectively, run out in 2017.
United face a huge decision when they do eventually decide to replace van Gaal at the club.
Many supporters would like to see Ryan Giggs manage the team but his appointment would be a gamble as he is yet to prove himself at the highest level. Van Gaal has done an excellent job of laying the groundwork and steadying the ship at United but you get the sense that the club will need an elite manager if they are to push on and reach the next level.