Adam Lallana and Luke Shaw look set to remain as Saints players going into the World Cup, with the club resisting their desire to be sold.
Lallana is the subject of a ‘take it or leave it’ £25m bid from Liverpool, while Manchester United have already lodged a £27m approach for Shaw.
Both players are understood to have informed Saints of their wishes to move on this summer and to speak with the respective clubs about a switch.
While both have an affinity to Southampton, they are keen to take up the chance of playing for two of the division's biggest teams.
Ideally, they would like the opportunity to do so before departing for Brazil next weekend.
However, Saints have now publicly declared that they intend to stand firm when it comes to their futures.
The club do not want to conduct any transfer dealings until a replacement for Mauricio Pochettino is appointed, saying they only allowed Rickie Lambert to leave for Liverpool yesterday as they felt that was a special case.
Saints are confident they are in a stronger position when it comes to Lallana and Shaw, and would also like to hold off until after the World Cup, knowing that there is strong interest in both and that, if they do have to sell them, their values could increase during the tournament.
A club statement said: “Southampton Football Club can confirm that we have received multiple offers for some of our players in the past weeks.
“This is a confirmation of the depth of the development that is ongoing in our academy and of the present standing of our first team within the Premier League.
“We are staying true to our plan and vision and, as a result, we have no need to accept any offers.
“It remains our preference not to partake in any transfers until the new manager is in place.”
Saints added that their new manager would have “final input” over recruitment matters.
Lallana and Shaw would both prefer to have their futures sorted before the World Cup begins, in which case a deal would need to be struck this week.
England, who are currently on a training camp in Miami, play warm-up matches against Ecuador and Honduras over the coming days, before they are due to arrive in Brazil on Sunday.
The national team manager, Roy Hodgson, has said he will allow clubs to fly staff out to Florida to conduct medicals, if necessary, as long as it is on the players’ free time.
But, while not certain, there is an increasing sense that such a point will not be reached with Lallana or Shaw, and both would be reluctant to take the step of handing in a formal transfer request.
From Saints’ point of view, the obvious downside to retaining the two players for now is that, should they be sold later this summer, as seems increasingly likely, it would reduce the time the club has to buy replacements, which could impact on their own pre-season preparations.