Saints are set to hand Martin the job of guiding the side back to the Premier League at the first time of asking, but he has not been given the role yet.
If Southampton were to appoint Martin now then they would need to pay Swansea more compensation than they would if they are a Championship club.
On 14th June, Southampton will officially lose their status as a Premier League side and drop into the Championship.
Then they will confirm Martin in the post and be due to pay Swansea compensation.
The Swans would have banked more compensation if Martin had already been appointed by Southampton.
They are already in the process of shortlisting candidates as they look at who the ideal man to succeed Martin is.
It is suggested they could announce their new manager at roughly the same time as Southampton confirm Martin.