Southampton have identified Lens manager Will Still as their leading candidate for the vacant position at St Mary's Stadium.
The 32-year-old, born in Belgium to English parents, announced last weekend he is leaving French side Lens to move back to the UK.
The move is complicated by negotiations that need to take place to free Still from his contract at the Ligue 1 club, which runs until 2027, as Lens could be due compensation.
In March, his partner Emma Saunders, a presenter on Sky Sports who previously worked for BBC Sport, said she was recovering from encephalitis, an infection of the brain.