The south-coast side drew plaudits for a string of excellent performances in the Premier League last season, as they achieved a record points tally in England's top flight.
Southampton's success has already seen Mauricio Pochettino depart for Tottenham last month, while England international Rickie Lambert joined boyhood club Liverpool earlier on Monday.
Rumours have also persisted that captain Adam Lallana will make the switch to Anfield, while full-back Luke Shaw is thought to be Manchester United's radar.
While revealing that offers have been received, a club statement rejected suggestions they could be forced to sell their prized assets.
"Southampton Football Club can confirm that we have received multiple offers for some of our players in the past weeks," it read.
"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. We are deep in the process of appointing a new manager who will continue to move our club forward.
"It remains our preference not to partake in any transfers until the new manager is in place. Our scouting & recruitment department continues to monitor targets we have identified to improve our squad, and the new manager will have final input into our recruitment process."
Southampton did, however, state that there are circumstances in which the club would accept bids, as was the case with Lambert who asked to join the team he supported in his youth.
The statement continued: "There may be circumstances under which the club will feel it is right for a player to move on. Those circumstances have to be right for the club and the player. This is the case with Rickie's move to Liverpool.
"When Rickie Lambert requested to leave for Liverpool, the club felt it could not stand in the way of having him fulfil his boyhood dream of playing at home.
"It will be a big challenge to replace him and our intention is to source a quality replacement who will fill his shoes now but also for many years to come."
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