If Cortese's departure is confirmed, Saints boss Mauricio Pochettino's future could be in serious doubt.
Sky sources indicate, however, that Cortese is not in discussion with another club in Italy, despite several media reports.
Cortese considered leaving St Mary's in May of last year after stressing to owner Katharina Liebherr that he was concerned about the future direction of the club.
At the time, Pochettino stressed that his involvement at Southampton was dependent on his chairman remaining at the club.
"If (he) Cortese doesn't work here... I would not understand a Southampton with Nicola being here," he said.
"The person who has put his faith in me at Southampton is Nicola Cortese."
Cortese, a former Swiss banker, fronted a deal on behalf of the Leibherr family to buy Southampton in 2009 when the club was in administration and in League One.
Since then, Southampton have spent more than £72million in the transfer market, breaking the club's record transfer fee three times - signing Jay Rodriguez from Burnley for £6m in June 2012, Gaston Ramirez from Bologna for £12m in August of the same year and then Dani Osvaldo for a fee reported to be close to £13m last summer.
There has so far been no comment from Southampton.
"....he was concerned about the future direction of the club" I thought being CEO meant you had a pretty strong say in the direction of any company? If something goes wrong, surely it his own fault.- FairyNuff