The attacking midfielder spent last season on loan at Torino and has been clear about wanting to return to the club this summer.
Torino allowed the €13m option to buy expire as they have been keen to sign him for a lower fee but West Ham rejected their offer of €9m.
Vlasic has been left fuming due to the dragged out nature of the negotiations and recently confronted David Moyes and the West Ham hierarchy to push for a transfer.
The Hammers have been clear about wanting more money and according to Italian daily Tuttosport (via Tutto Mercato), Torino have tabled a fresh offer.
It has been claimed that the Serie A outfit have offered €10m to West Ham for the signature of Vlasic.
With no other offers on West Ham’s table for the Croatian, Torino are confident that they will get their man.
The attacking midfielder is pushing to return to Torino and has been putting pressure on West Ham.
It remains to be seen whether the Hammers agree to let the player go for less than €13m this summer.
