Vlasic is subject to interest from Torino this summer after the midfielder impressed the Turin outfit during his loan spell with them last season.
Torino let an option to buy clause in Vlasic’s loan deal lapse as they are hopeful of getting the player for a lower transfer fee.
West Ham have slapped a €13m price tag on the player and they have rejected Torino’s €10m offer for Vlasic.
The Croatian midfielder has made his desire to leave the club clear to Hammers boss David Moyes and technical director Steiden.
However, West Ham are insisting on their valuation and have no problem playing the waiting game.
Now, according to Italian daily Tuttosport (via Tutto Mercato), the West Ham hierarchy have instructed Steiden to open fresh talks with Torino to facilitate a return for Vlasic to Turin.
It remains to be seen whether both clubs will finally be able to come to an agreement on a transfer to seal the deal for the midfielder.
Last season, Vlasic featured 35 times in the league for the Italian outfit, scoring five goals while assisting six.