The Gabon international is expected to undergo a medical at St Mary's on Monday (7 August), after the two clubs reportedly reached a deal over the weekend. Lemina, who represented France at Under 21 level, was not included in Juventus' squad for their friendly against Tottenham Hotspur at Wembley on Saturday (5 August) and is expected to become Southampton's second summer signing after Polish defender Jan Bednarek.
The 23-year-old, who was subject of an offer from Leicester City last summer, will cost the Saints an initial £18m and further £2m in add-ons, a total fee which will surpass the £17m the club paid Lille for Sofiane Boufal last summer, according to The Mirror.
Lemina, who was also on Watford and Stoke City's radar, joined Juventus for £7.5m last summer from Olympique Marseille, having spent the previous season on loan at the Serie A champions. During his spell in Turin, Lemina won two league titles and two Italian cups and was a second half substitute in last season's Champions League final, as Juventus lost 4-1 to Real Madrid in Cardiff.
The midfielder began last season in promising fashion, starting six out of Juventus' first eight Serie A games, but was included in the starting eleven only three times in all competitions between December and May.
Mauricio Pellegrino, who replaced Claude Puel in the St Mary's dugout earlier this summer, said he was hopeful the new signings will make a good impact. "Hopefully the players that come in will make us stronger," he said ahead of his first season at the helm.
The Saints, who finished eighth in the Premier League last season and lost the English Football League Cup final to Manchester United, are desperate to hold onto Virgil van Dijk, who has made clear he want to leave the south coast and join Liverpool.
The Holland international has attracted interest from a number of Premier League sides, but Southampton remain adamant that they will not sell the £60m-rated defender this summer.