Southampton insist Virgil van Dijk and Cedric Soares are "not for sale" amid reports the club have agreed with new manager Mauricio Pellegrino that they will not allow star players to leave.
Liverpool, Manchester City and Chelsea are being linked with swoops for Van Dijk, while Barcelona, Juventus and Tottenham are among the clubs said to be chasing Cedric.
But Les Reed, Southampton's executive director, insists his club have no plans to sell and hopes to have a quiet transfer window.
"None of those players are for sale," Reed said to Sky Sports. "I can't make it any plainer than that and that's the way we mean to go forward.
"We built this squad over some time and think we have a strong squad. We will fine-tune it but, other than that, we are looking forward to a very competitive season next year and we plan to go forward on that basis.
"It's not broken so there is no need to bring in players just because of fashion or to get people excited in the transfer market."
Former Alaves boss Pellegrino signed a three-year contract to replace the sacked Claude Puel last week.
"We track players over years and when the new manager comes in like Mauricio, we take him through that process," said Reed.
"He'd done his homework on our squad and we don't believe we need to turn over players every year just to freshen things up.
"There may be players that go on the basis it is the right thing for them and the club at that given time, but we don't expect that to be wholesale and this is simply doing sound business in the transfer window.
"We've got a strong squad now and it would be about adding players bringing more value and power."
Reports linking Van Dijk to Liverpool continue despite the Reds stating they have dropped their interest in him earlier this month, having apologised to Southampton for "any misunderstanding" surrounding their pursuit, following an alleged illegal approach.