The Hammers have made an impressive return to the top-flight of English football this season and have the chance to finish in the top half of the table with victory over Reading at Upton Park on Sunday.
It is understood that the east London club have offered the 35-year-old a two-year deal to play in the Premier League, with his current contract with the Serie A giants set to run out next month.
The multiple Champions League and Serie A winner was expected to see his career out with the Rossoneri but he could be tempted to prolong his playing days with a spell in England.
Roggi said: “There is interest from West Ham and it’s a real interest, like that of other English, German and American teams, although there have not been concrete contacts.
“But, like every year, the first thing Massimo will do at the end of the season is speak with Adriano Galliani (AC Milan CEO).”
Bayern Munich have entered the race to Emre Can, who continues to talk up a move away from Liverpool this summer.