Allegri was axed after three and a half years on the Rossoneri bench following a humiliating 4-3 loss to Sassuolo, which compounded a miserable Serie A campaign to date.
There was little surprise across the peninsula at the news given that Allegri had been frequently tipped to lose his job at the end of 2013 and the start of 2014.
Mauro Tassotto has been given interim control of the squad and will seek to steady the ship as soon as possible, but the club are busy selecting a new long-term boss.
The choice is believed to be between two former Milan players - Dutch midfielder Seedorf and striker Pippo Inzaghi.
But Inzaghi, who is currently in charge of the Diavolo youth team, seems to have fallen by the wayside with almost all of Italy's major newspapers reporting the imminent arrival of Seedorf.
Seedorf is playing for Brazilian side Botafogo but he has started studying as a coach and his agent has stressed that his contract allows him to liberate himself at any time as long as he doesn't play elsewhere.
While La Gazzetta dello Sport believes Seedorf will arrive on Thursday to start a new era, Sportmediaset reports that he will land in Milan tomorrow on a two-and-a-half year contract and he will bring with him Jaap Stam to look after the defence and Hernan Crespo for the attack.
However, so far Seedorf has refused to discuss the Milan bench, insisting that he isn't allowed to, so official confirmation will have to wait.
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