The Rossoneri coach could be axed if he fails to guide the club to their second consecutive Scudetto following their early Champions League elimination to Barcelona
The 44-year-old only recently signed a contract extension with the Rossoneri until June 2014, but their Champions League quarter-final exit against Barcelona has supposedly angered president Silvio Berlusconi.
The former Prime Minister of Italy was not impressed with Milan's performance against the Catalan giants, and is considering giving his coach the sack unless they win the Scudetto again.
Allegri joined Milan from Cagliari in the summer of 2010 and guided them to their first league title since 2004 in his first year in charge at San Siro.
However, the Rossoneri have failed to impress in the Champions League since he took the reins, crashing out at the round of 16 stage last season before this year's quarter-final exit. As a result, Berlusconi is now believed to have doubts about whether Allegri is the right man to lead Milan back to the top of Europe.