Rumours have been circulating that Allegri will be relieved of his position after a poor start to the season, but the experienced manager has received the backing of club owner Silvio Berlusconi.
"I met president Berlusconi in the changing rooms, and he told me he was happy with the performance," Allegri told reporters.
"There have been countless names and rumours circulating. The story bores me a bit and it's up to the club to deal with these situations."
Former Barcelona boss Pep Guardiola has been linked with the post.