Former Alaves coach Mauricio Pellegrino is in advanced talks with Southampton over the manager's job.
The Daily Echo says Saints have been busy conducting interviews over the past few days, and they are edging nearer to a decision.
It is believed the shortlist has now been whittled down to just three contenders, with Pellegrino and Frank De Boer the clear favourites.
There is a sense that Pellegrino could emerge as first choice, but the situation is complicated by the fact that Crystal Palace are also believed to be keen on him for their own managerial vacancy.
It is believed that De Boer has also been interviewed by the Eagles.