Mane joined the Saints for a reported £10.8m from Red Bull Salzburg on deadline day but is yet to make an appearance after failing to secure the necessary clearance.
Koeman admits that Saturday's trip to Swansea City comes too soon for the 22-year-old, but says that he could make his debut in Tuesday's League Cup clash away at Arsenal.
"Yesterday I got a message that everything is done and the work permit is okay," the Dutchman told reporters.
"He is flying back today and will arrive tomorrow very early but it's too close for Saturday.
"Tomorrow I'll speak to him about his physical state because I don't know what he did in the last 10 days, but it will be a good chance for him to be part of the squad for the League Cup game against Arsenal."
The Senegal international struck 45 times in a two-year spell with the Austrian champions.