Vlasic spent last term on loan at Torino in Serie A and has been desperate to return to the Italian side this summer.
Torino have held talks with West Ham over several weeks and have now achieved a breakthrough, with a permanent move for Vlasic set to happen.
A fee of £11m has been agreed between the two clubs, according to Sky Italia, and Vlasic is now booked in for a medical.
Vlasic will be put through his medical paces by Torino on Tuesday.
Should he come through the medical without an issue, he will then put pen to paper to a contract with Torino and end his association with West Ham.
It will mean further money flowing into West Ham’s coffers this summer.
The London side have already sold Declan Rice to Arsenal and also cashed in on striker Gianluca Scamacca, who has been sold to Atalanta.
