The 33-year-old Netherlands international spent the 2015-16 campaign at St Mary's on loan from Fulham and the Liverpool Echo report that Ronald Koeman is looking to bring Stekelenburg in as a back-up to a potential new Number One he is currently planning.
That would place a big question mark over the future of Joel Robles just months after he had finally made the first-choice goalkeeper's jersey his own following almost three years awaiting his chance behind Tim Howard.
“If you look at the squad you see one goalkeeper," Koeman says in the Echo. “You can't start a season with one goalkeeper. But it is not about ‘we need a No 2, we need a No 3 or we need a No 1'.
“No, it is all about numbers of goalkeepers but first of all we need to talk with the people at Everton because I like to hear their opinions because it is important for me to make my decisions.”