Mane is still awaiting his Saints debut after joining the club from Red Bull Salzburg in an £11.8million deal, but will not feature against Swansea on Saturday.
Koeman said: "Yesterday I got the message everything is done
The work permission is okay.
"He is flying back today and he will arrive tomorrow
It's too close for Saturday."
Koeman will assess 22-year-old Mane's physical state before determining if the winger can feature against Arsenal in the Capital One Cup next Tuesday night.
"The last 10 days I don't know what he did," Koeman added.
"It will be a good chance for him to be part of the squad for next Tuesday, for the League Cup game against Arsenal."
Saints have no injury concerns after striker Shane Long overcame a head injury.
"Shane Long is okay," Koeman added.
"He's (been) doing training sessions for three days
He's no problem for this Saturday
No injuries
Only the case of Mane."
Mane's transfer is the sort which may not occur if the Football Association succeeds in tightening rules over non-European Union imports.
Koeman, though, defended Southampton's impressive record of nurturing native English talent.
"I'm positive to try in the country to do the maximum for the English players," the Dutchman added.
"I think we do that in Southampton
If you look at the team, our squad, it's a lot of English players, a lot of young players, maybe it's more and more than the rest of the clubs."
Source : PA
Source: PA