Mauricio Pochettino has said he will leave Southampton if executive chairman Nicola Cortese departs.
There is a break clause in Cortese's contract that can be activated either by the Italian or the club's owners, the Liebherr estate, this summer. The Press Association claims he is considering an exit over the backing he receives from the club as he looks to establish the Saints as a Premier League force.
The Daily Echo newspaper in Southampton reports that a decision will be made by the end of next month at the latest.
Cortese attracted criticism when making the decision to dismiss Nigel Adkins in January despite the manager leading the club from League One to the top flight. He was responsible for the appointment of former Espanyol manager Pochettino, who guided the club to Premier League safety this season and has spoken of his desire to guide the club into the Champions League in the imminent future.
However, asked if he would stay at St Mary's if Cortese left, the Argentinian said: "Of course not, because the person that has put his faith in me in this club and as a manager is Nicola Cortese.
"Nicola Cortese has basically been the reality at Southampton for the past four years. Of course, the people that are in the club, that are part of the club, that are behind the scenes in the club were a little bit worried about what has been said.
"Me on a personal sense, I would not understand a Southampton without Nicola being here."
Information from the Press Association was used in this report