Adam Lallana and Luke Shaw have both told Saints they want to move this summer.
But they both 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 speak with the respective clubs about a switch.
Ideally, they would like the opportunity to do so before departing for Brazil next weekend – although they have not submitted formal transfer requests.
Lallana, though, is reportedly unhappy that Saints didn't return his calls last weekend as he tried to engineer talks with Liverpool.
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.
Lallana and Shaw would both like 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 - as Wayne Bridge was forced to do back in the summer of 2003.
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.