The Serie A side were keen on snapping up Vlasic earlier in the window on a permanent basis but a deal was rated as complicated as they were not able to fork out a huge fee for him.
With less than a month left in the transfer window, Torino are again keen on snapping up the Croatian from the Hammers but on a temporary basis.
Torino technical director Davide Vagnati is working on a loan deal for Vlasic as he looks to provide coach Ivan Juric with a stronger side.
But according to Sky Italia, Torino are still struggling to get a deal over the line for the Hammers man, as there is intense competition for his signature.
West Ham are open to offloading Vlasic, and could even allow him to leave on loan, but he is not short of suitors in the ongoing window.
Vlasic is not part of David Moyes’ plans at the London Stadium this season but a move to Torino is likely to earn him game time on a regular basis.
The 24-year-old did feature under Moyes in pre-season games, and it remains to be seen whether he will remain at the club beyond this summer.
