The former Marseille man is expected to undergo a medical on Monday.
West Ham have been keeping tabs on him, while Stoke City have even tabled a bid for the player and have requested a meeting with Juventus officials imminently.
The package being put in place includes an additional €2m in bonus payments.
The 23-year-old was reportedly on Southampton's radar before he elected to move to Juventus where he has won two league titles and two Coppa Italia cups.
Lemina joined Juve from Marseille in the summer of 2015, and the versatile midfielder made 29 appearances in all competitions for the Italian champions during the 2016-17 campaign.
Saints are understood to have agreed a £16million fee for the Gabon global, who made a substitute's appearance in last season's Champions League final in Cardiff.
He will now be hoping to see more minutes with Southampton, with Mauricio Pellegrino's side set to seal a transfer before the start of the new Premier League season.