Mane, 22, joined Southampton from Red Bull Salzburg on transfer deadline day in a deal reportedly worth £11.8 million, but he has yet to make his debut for the club.
Having been granted a work permit, he will join up with his new teammates on Friday, but Koeman said that he was not in contention to face Swansea City in the Premier League on Saturday.
"Yesterday (Wednesday) I got the message everything is done. The work permission is OK," Koeman told a press conference on Thursday. "He is flying back today and he will arrive tomorrow. It's too close for Saturday."