Two separate articles on the Italians' official site made reference to the Caen striker, who has already represented France at under-21 level, saying he dined with vice-president Adriano Galliani last night and is set to undergo a medical today.
"Adriano Galliani flew into Milan last night and immediately went to a restaurant with new signing M'Baye Niang," the club said.
"Today he will have to pass his medical."
Niang has been with Caen since he was 13, but only turned professional last season and has also previously been linked with a move to Arsenal.
Milan also said Galliani had declined to make a move for Real Madrid midfielder Kaka - a former world player of the year during his time at the San Siro.
Meanwhile, Kevin Mirallas could be handed his home debut when Everton face Leyton Orient in tomorrow night's Capital One Cup second-round tie.
The Belgian striker came off the bench to feature in the last 20 minutes of the 3-1 win against Aston Villa on Saturday following his £5.3million move from Olympiakos.
Tony Hibbert is the only injury doubt despite David Moyes naming an unchanged squad for the visit of the League One outfit.
Provisional squad: Howard, Baines, Distin, Jagielka, Hibbert, Neville, Gibson, Fellaini, Pienaar, Osman, Jelavic, Naismith, Mucha, Heitinga, Coleman, Anichebe, Barkley, Gueye, Mirallas.