Sky Sportsreports that the Hammers will put forward an offer of £30m for the Albania international.
That is despite the uncertainty surrounding Chelsea director Marina Granovskaia.
Granovskaia's future is up in the air following Bruce Buck's departure at the end of this month.
A decision on Broja will then rest on the shoulders of new owner Todd Boehly and manager Thomas Tuchel.
20-year-old Broja impressed on a season-long loan at Southampton last season, scoring nine goals in 38 appearances.
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