The Argentina looks set to leave the Italian champions at the end of the season after a complicated campaign.
He has only managed 14 appearances throughout, as injuries have seriously limited his game time.
Juventus are keen to move him on, as they eye a move for a quality midfielder themselves, either Miralem Pjanic or Andre Gomes.
Despite a difficult year, Pereyra has a decent market value and they are confident of finding a club for him.
West Ham are interested according to Tuttosport, and are willing to pay as much as €13million for his services, around £10.2million.
Juventus reportedly want a couple of million more for their midfielder, but it is believed that an agreement between the two sides is more than possible.
Slaven Bilic’s side are keen to improve their squad in the summer after an impressive first campaign under the Croatian, and Pereyra could the first of several new faces at the club as a result.