After scoring three goals and providing seven assists in the 2020/21 Ligue 1 season, Perraud made his way onto the transfer wish list of several Premier League clubs.
Leeds are looking to sign a left-back and have been strongly linked with wanting the 23-year-old, but Southampton are poised to beat the Whites to him.
Southampton, who view Perraud as an ideal replacement for Ryan Bertrand, appear to have won the race for the left-back as they are close to striking a deal with Brest.
According to French sports daily L’Equipe, the Saints and Brest are still locked in negotiations as they look to iron out the final details of the deal.
While an £8.5m fee have been mooted, Brest expect to bank a total fee in excess of €12m, which accounts for around £10.3m, for the sale of the left-back.
It remains to be seen if that sum is what the French top flight club expect to earn from Southampton after potential bonuses and add-ons.
Regardless, no hiccups are expected in the talks between the two clubs and Perraud is tipped to be a Southampton player soon.