The 26-year-old winger is not in Saints boss Ralph Hasenhuttl’s plans for the season and is expected to be on his way out of St. Mary’s before the transfer window closes.
Greek top flight club Olympiacos have expressed interest in acquiring the services of Boufal and are in talks with Southampton over a deal for him.
As talks progress between the two clubs, the Attica-based side have agreed personal terms with Boufal, who is now edging closer to a move to Greece.
The Morocco international has entered the final year of his contract with the Saints and the Premier League club will want to recoup at least a part of the sum they paid for him four years ago.
Southampton signed Boufal from French Ligue 1 club Lille for a fee in the region of £16m in the summer of 2016, making him their most expensive signing at the time.
He spent the 2018/19 campaign on a loan stint in Spain at Celta Vigo, but headed back to Southampton last summer.
The Morocco international clocked 25 appearances across all competitions for Southampton over the course of last season.