Vlasic, 25, joined Torino on a season-long loan deal from West Ham last term and enjoyed an impressive campaign with the Turin-based side.
Now the Serie A outfit is keen on bringing the Croat back to the club again this summer but they did not trigger their option to buy as they believed it was too expensive.
Moyes’ side want a fee worth €13m for Vlasic and Torino consider the price too high to fork out, with the midfielder himself eager to make an exit from the London Stadium.
The Italian side are seeking to reduce the price for the Croat, with the midfielder said to be frustrated with the transfer scenario.
According to Italian daily Tuttosport, Vlasic had a confrontation with Moyes and Steidten with his efforts to move on to pastures new continuing.
Vlasic made clear that he wants West Ham to sell him to Torino and pushed for the move.
Torino have already seen their initial offer of €9m for the Croat turned down by the Hammers and the player is hoping to see his future sealed soon.
Now it remains to be seen whether the two outfits will be able to reach an agreement over the fate of the Croatia international in the coming days, with the clock ticking down on the ongoing transfer window.