The Turkey international has struggled for form this season and could be set to switch Serie A for the Premier League.
Turkish outlet Fanatik has reported that the £26 million-rated attacking midfielder has caught the attention of both the Hammers and Foxes.
Both sides are looking to bolster their squads for next season, with five points currently separating 10th-placed Leicester from West Ham in 11th.
Calhanoglu joined the Rossoneri from Bayer Leverkusen in the summer of 2017 and has scored one goal in 31 league appearances this season to help Milan to fourth place in the table.
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