Former Brighton manager Oscar Garcia is believed to have been sounded out about the vacant Saints job.
An initial check on the Spaniard is understood to have taken place, although no serious approach has been made as yet.
It is something that Saints will no doubt be doing with a large number of people, as they sound out interest and availability of possible replacements for Mauricio Pochettino, after he resigned to join Spurs this week.
As revealed by chairman Ralph Krueger yesterday, Saints have started the process of searching for a new boss by putting together a prospective long list of names.
That will be whittled down over the coming days.
Garcia is one of many people thought to be on that initial list, and it is understood the 41-year-old would have an interest in the job, although he is believed to have other opportunities too, with Celtic one club rumoured to be interested after the departure of Neil Lennnon.
Garcia joined Brighton last summer, but left his post this month after the club lost to Derby in the Championship play-off semi-finals.
Former Basel manager Murat Yakin and Feyenoord coach Ronald Koeman are the early favourites with the bookies for the Saints job.
Yakin has already declared an interest in the position, while Koeman would be open to a switch to England.
Michael Laudrup, who was dismissed by Swansea in February, but who delivered a Capital One Cup trophy success and who won plaudits for his style of play with the Welsh club, is also high on the list of favourites.