Vlasic, 25, joined the Hammers in 2021 from CSKA Moscow on a five-year contract, but the Croat was unable to live up to expectations at the London Stadium in his debut season.
He was shipped out to Torino last year, with the Italian side holding an option to buy the Croatian midfielder at the end of the loan.
Vlasic has contributed significantly to the Italian outfit’s Serie A campaign this season as the midfielder has bagged five goals and four assists in 32 league matches besides getting booked once.
And according to Italian daily Tuttosport, the Turin side are keen to discuss with the Hammers how that price can be lowered by the London outfit.
Torino want to sit down at the negotiating table with West Ham and find a deal that works for both parties.
However, it remains to be seen whether West Ham work to lower the price of Vlasic or the Italian side look elsewhere to bolster their midfield ranks this summer.