Virgil van Dijk claims he knows nothing of interest from English clubs and is keen to prove himself in the Champions League with Celtic.
QPR loanee Tom Carroll wants to "make it at Tottenham" but is prepared to consider all of his options at the end of the season.
Honorary president Terry Paine has warned that Southampton will return to the "dark days" of League One without executive chairman Nicola Cortese.
The Italian businessman was an integral part of Markus Liebherr's takeover in 2009 and stayed on after the Swiss billionaire died suddenly the following year.
However, having helped the club rise from the third tier to the Barclays Premier League, Cortese is understood to be considering his position due to frustrations over the backing he receives.
The executive chairman will make a decision on whether to remain at the club within the next month and record appearance holder Paine, appointed honorary president in December, has highlighted his importance.
"Southampton cannot do without Nicola Cortese," Paine told BBC Radio Solent.
"The chairman has made two or three brilliant decisions that may not have looked like it at the time but now it has come to fruition and we realise just what impact he has had and thank goodness for that.
"We do not want to be back to them old dark days where we were three years ago.
"He has taken us to where we are now by making some great decisions and some difficult decisions.
"We cannot rest on our laurels because he is the only one with the vision to take us further, that is why he has brought in the new manager. That is another part of his vision.
"He just can't leave. I believe if he leaves then in three years we will be back where we started [League One]."
Cortese's departure would seriously impact Southampton, with manager Mauricio Pochettino yesterday confirming he would follow Cortese out of the club should he leave.
"It is a fact," Paine added. "The manager has said he will leave and you can understand that.
"He [Cortese] has set out a plan for the manager, he has brought him on board. He [Pochettino] won't be short of jobs as he is a top, top coach.
"That was a coup in bringing him in and if he leaves then we will be back to square one."
The repercussions of Cortese and Pochettino leaving would be wide-ranging and fly in the face of the much-spoken-about 'project' at Southampton.
Regularly mentioned by players and staff, it is part of the reason why player of the year Morgan Schneiderlin recently signed a new deal at the club despite reported interest from Arsenal and Inter Milan.
"Of course I would be upset if that happens," said the Frenchman, whose immediate focus is Sunday's season finale against Stoke.
"The chairman and Mauricio Pochettino are a big part of this club.
"They are selling a project to us and that is why I signed a new contract, that is why other players signed contracts.
"They are a main part of Southampton Football Club for the future if we want progress and to reach where the chairman and the manager want to, then I think it is very important that they stay.
"Of course it would put everything in question again but I am sure that won't happen."