West Ham, determined to strengthen their strike force this season, are understood to have indicated they are willing to pay an initial £25m plus £5m in add-ons for the young striker.
Broja, 20, is currently on Chelsea’s pre-season tour in America during which manager Thomas Tuchel was keen to assess him before making a decision on his future.
However West Ham have made their move to see if they can persuade Chelsea to sell him this summer. Talks are ongoing.
Broja has other admirers along with West Ham, including Everton and Newcastle, following an eye-catching loan spell at Southampton last season.
Broja has four years left on his current Chelsea contract after signing a five-year deal last summer ahead of joining Southampton.
As well as those two bids, they have a £33m bid on the table for Sassuolo striker Gianluca Scamacca who has been of interest to PSG.
Scamacca – who was also scouted by Arsenal earlier on in the window – scored 16 times in 36 Serie A appearances last season.
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