The Hammers are set for a summer of significant changes after finishing 13th this term and a large amount of transfer activity is expected.
Manager Sam Allardyce could be axed, prompting a full-scale clear-out of players who are surplus to requirements to allow new faces to be brought in.
West Ham signed Italians Antonio Nocerino and Marco Borriello on loan in January, but both could return home without having made the impression they hoped for, even though Nocerino is keen to stay.
Montpellier haven't attempted to keep the 19-year-old beyond his loan spell which saw him score four goals in 13 games.
Primarily a striker, Niang can also play on the wing and in the past has won comparisons to Mario Balotelli.
The Frenchman joined Milan from Caen in 2012 after trials at Arsenal, Everton and Tottenham and became the second youngest player to score for the Rossoneri at the age of 17 years and 350 days when he netted against Reggina in an Italian Cup game in December 2012.
Niang is set to return to Milan this summer to await news of his future and it is reported that West Ham have already opened talks over a loan.