Swansea have put a £50 million price tag on Gylfi Sigurdsson amid interest from Everton and Leicester, according to multiple reports.
Swansea remain determined to keep hold of Sigurdsson, who was named the club's player of the year for the second successive campaign last season.
The 27-year-old scored nine league goals and provided 13 assists in a team which spent the entire season battling against relegation.
PA Sport reported that Swansea wanted at least £40m if they were to sell Sigurdsson, who has three years left on his contract.
He has scored 30 goals in 112 games since the Swans signed him from Tottenham for £6.8m in July 2014.
Swansea chairman Huw Jenkins said in February that Sigurdsson was the subject of "substantial offers" during the last transfer window, with interest reportedly come from both home and abroad.
Sigurdsson said at the club's end-of-season awards in May that he was happy at Swansea and would only leave the Liberty Stadium if the club wanted to sell him.
Everton have spent big in the summer transfer window so far with Jordan Pickford, Davy Klaassen, Michael Keane, Henry Onyekuru, Nathangelo Markelo, Sandro Ramirez and Wayne Rooney all joining.
The Toffees' coffers are also set to be swelled by the sale of striker Romelu Lukaku to Manchester United for an initial £75m.
Leicester have also been strongly linked with Sigurdsson, particularly as Riyad Mahrez's future has been in doubt after he asked to leave.
Swansea midfielder Jack Cork, meanwhile, is in talks to join Burnley, a club where he has had two previous loan spells.
Cork, 28, has played 80 league games for Swansea since joining from Southampton in a £3m deal in January 2015 but he lost his first-team place as Swansea secured their top-flight survival under Paul Clement.
And Cork's game time could become even more limited following the £11m signing of Las Palmas midfielder Roque Mesa.