Conceicao was hired on Monday following the dismissal of Paulo Fonseca.
But Il Corriere dello Sport says Milan were criticized by another coach just over a week ago.
On December 24, Milan offered a contract to former Lazio coach Sarri, but was rejected.
Sarri was offered a contract until the end of the season, with an option for a further year.
However, the 65-year-old had hoped for a longer contract and was therefore not interested in the assignment.
Conceicao has signed a deal until June, with an option for a further twelve months.
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