West Ham brought in the 25-year old attacking midfielder from CSKA Moscow in the summer of 2021, but the player struggled to get into David Moyes’ starting line-up.
Vlasic went out on loan and joined Italian outfit Torino in search of regular football last summer.
He has been a key part of Ivan Juric’s starting line-up this season and has made 31 outings for the club, registering five goals and four assists.
Juric considers the West Ham loanee an integral part of his squad and wants to sign the midfielder on a permanent deal.
Vlasic has a €13m option to buy clause in his loan contract, however, according to Italian outlet Calciomercato.com, Torino will ask West Ham to reduce the transfer fee for the midfielder.
The Italian outfit want to renegotiate the transfer fee for less than €10m and it is unclear whether the Hammers are willing to do so or not.
Vlasic is enjoying his football with the Italian outfit and is in favour of a permanent move to Turin in the summer.