It had been claimed that the Sweden international, who has been linked with a move away from San Siro, has fallen out with his boss and several team-mates
The pair's relationship has completely broken down, with the Rossoneri coach also said to have informed club owner Silvio Berlusconi that the Swede has fallen out with a number of his team-mates, according to ANSA.
The report claimed that Allegri, in conjunction with CEO Adriano Galliani, told the honorary president that the 30-year-old forward's position within the squad is no longer tenable.
The coach also reportedly urged the club to consider cutting their losses on the player this summer in light of Ibrahimovic's age and the fact that he is just coming off the back of the most prolific season of his career.
However, Milan have now hit back, issuing a brief statement on their website claiming that ANSA's report is "without any foundation and is not true."
Allegri claimed on Monday that he felt lucky to have Ibrahimovic within his squad and was delighted that the striker had publicly stated that he would be staying at San Siro following reports linking him with a reunion with his former Inter boss Jose Mourinho at Real Madrid.
Ibrahimovic, who joined the Rossoneri on loan from Barcelona in 2010 before the move was made permanent last summer, hit 28 goals in 32 Serie A appearances this season.