West Ham are said to be keen but face competition from a host of clubs across Europe.
Juventus are looking to sell Lemina to free up more funds to spend on strengthening their side for next season.
This is despite having just sold Leonardo Bonucci to rivals AC Milan for a fee in the region of €40m.
Juventus are interested in Fiorentina’s Federico Bernardeschi and are looking to sell Lemina to fund their move.
Hammers boss Slaven Bilic is looking to make two major additions to his starting eleven for next season, with Lemina possibly one of them.
Joe Hart is expected to sign on a season-long loan in the coming days.