Vlasic spent last season on loan at Torino and has been clear about wanting to stay at the Italian club.
Torino allowed their option to buy him to lapse last month but are still interested in signing him on a permanent deal and have been confident about doing so.
But they are yet to meet West Ham’s €13m asking price with the Hammers rejecting their latest bid of €10.5m recently.
Torino are pushing to sign him but according to the Turin-based daily Tuttosport, they have now set a deadline for the swoop.
They are in constant talks with West Ham over working out a compromise but a deal is still not close to getting agreed.
Torino have made it clear that they are keen to find a resolution one way or the other for Vlasic before next Monday or Tuesday.
It has been suggested that they could move on to other targets if a deal cannot be agreed for Vlasic’s transfer by early next week.
