Reports in the press are rife suggesting that United are ready to replace Ole Gunnar Solskjaer with the Italian, who is currently a free agent after leaving his job with Juventus at the end of last season.
Ed Woodward has insisted that United will stick with Solskjaer as they look to take the club in a new direction and will stick to the plan, but that is not stopping suggestions that a change in manager will be made sooner rather than later.
It has been claimed that talks have already taken place with Allegri with a view to him replacing Solskjaer, but the Italian tactician was quick to dismiss such talk.
"I don't speak English enough yet, but I'm learning," Allegri has been quoted as saying.
Emphasis has to be placed on the word yet.
The former AC Milan coach is known to have been learning English with a view to one day managing in the Premier League, and he is sure to be interested in the United job should it become available down the line.
Whether Allegri would be deterred by the fact that big names such has Louis van Gaal and Jose Mourinho have already been axed by the Reds, remains to be seen, but he could be offered the opportunity at some point.
Other jobs could of course become available and the Italian has also been linked with replacing Mauricio Pochettino at Tottenham should he move on.
Allegri will not be without a job for long and United may be thinking they have to move soon if it looks as though things will not improve with Solskjaer in charge.
A lot could hinge on this weekend's big clash against Liverpool at Old Trafford when a bad result will put another nail in Solskjaer's coffin.