Conceicao was hired on Monday after the sacking of Paulo Fonseca.
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But Il Corriere dello Sport says Milan received a snub from another coach just over a week ago.
On December 24, Milan offered a contract to former Lazio coach Sarri - but received a rejection.
Sarri was offered a contract that ran until the end of the season, with an option for another year.
However, the 65-year-old had hoped for a longer contract, and thus he was not interested in taking on the assignment.
Conceicao has penned a deal to June, with an option for another 12 months.