Southampton say they would prefer not to sell any more players before appointing a new manager, after allowing Rickie Lambert to join Liverpool.
Saints have received "multiple offers" for their stars in the transfer window while the move for Lambert - for an undisclosed fee - was completed on Monday.
The 32-year-old England forward passed a medical over the weekend before flying out to Miami with Roy Hodgson's squad to continue preparations for the World Cup in Brazil.
Liverpool are also tracking Saints captain Adam Lallana, with a fresh £25m bid reportedly lodged with Southampton's owner Katharina Liebherr.
England left-back Luke Shaw is reportedly being pursued by Manchester United, while forward Jay Rodriguez could follow former boss Mauricio Pochettino to Tottenham.
An official Southampton 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. 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 and 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."
Saints paid tribute to Lambert, who helped the south coast club return to the top flight from League One, after the Liverpudlian returned to Anfield.
Lambert is understood to have signed a two-year deal, for a transfer worth around £4m, with the club who released him as a 15 year-old.
"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," Southampton's statement continued.
"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."
Chairman Ralph Krueger said: "On behalf of the club, I would like to thank Rickie. He served with distinction and helped to take Saints from League 1 to the Premier League.
"Rickie has been a shining light in Saints' growth and will forever remain an icon in the history of the club. He leaves with the best wishes of everyone at Southampton and will always be welcome back at St Mary's."
Last week, Krueger claimed Southampton had been inundated with calls from some of the "highest quality managers in Europe" and that the club are in their best ever position despite Pochettino's exit, having finished eighth in the Premier League last season.
Former FC Basel coach Murat Yakin and Dutchman Ronald Koeman are the current bookmakers' favourites to take the St Mary's hotseat, while former Swansea manager Michael Laudrup is also said to be in the running.