However, club chairman Huw Jenkins has said they will fight to keep Gylfi Sigurdsson, Alfie Mawson and Fernando Llorente at the Liberty Stadium.
Keeping key trio
Jenkins says Swansea are determined to keep hold of their star players, despite Everton being linked with a £40m move for Sigurdsson and England Under-21 defender Mawson apparently attracting Tottenham Hotspur.
Spanish striker Llorente has also been mooted for a move with the Swans reported to be ready to offer him a new contract.
“Keeping your top players is always a difficult one,” Jenkins said.
“It is a slow market as the players have been away on international duty. We want to keep our best players and to that end Gylfi Sigurdsson and Fernando Llorente had good seasons with us last year.
“Naturally that causes interest and there is plenty of media coverage, but our aim is to keep our best players and try to add to that.
“We aren’t putting figures on our players. We see the figures bandied around in the Premier League and they are crazy, but we are part of that.
“We will do our best to add to the team, not take away from it.
“We’ve had no direct contact from any club, it is pure speculation and we hope it remains so.”
On apparent Spurs target Mawson, who only joined last summer from Barnsley, Jenkins added: “There has been no firm interest, but his profile is being raised, we understand that.
“But we think he’s got a few years left with us to develop his career.”
Spine of the side is a priority
Jenkins says Swansea are looking for additions in central midfield and attack, but France striker Bafetimbi Gomis is unlikely to be under consideration for a return after a loan season with Marseille.
“Gomis (moving) to Galatasaray is possible, we have been talking,” Jenkins confirmed.
“Paul has a fair bit of money to consider and there are one or two players we are looking to get signed.
“The main positions we are looking for (with the way that we play) is a central midfielder and a second striker.
“Those are our main focuses, but there may be one or two other areas if some fringe players leave the club, as some last year didn’t get enough game time.
“We need to make sure we freshen the squad up and the American investment has provided the club with financial stability, we are paying out for contracts bigger than ever before.”