Glasgow Rangers, a Scottish Premiership team, and Joe Aribo, a Nigerian player, have agreed on a price.
The Athletic reports that the Saints will make an initial £6 million payment for the 25-year-old.
With add-ons, the cost might reach £10 million.
Aribo’s contract contains a £10 million release clause, and Rangers were adamant not to trade him for less.
Despite apparently reaching a personal agreement with Southampton, the player has not yet signed a deal with the Premier League team.
Last season, in 57 appearances for the Gers in all competitions, Aribo contributed nine goals and nine assists.
He signed a four-year contract to join Rangers from Charlton Athletic in 2019.