Swansea owner Steve Kaplan has told WalesOnline that the club "don't want to sell" Gylfi Sigurdsson this summer, amid reports of interest from Tottenham and Everton.
It was claimed on Tuesday that Swansea had agreed a £25 million fee with Everton to sell Sigurdsson, 27, but Swansea want to keep a player who scored nine goals and provided 13 assists in the 2016-17 Premier League season
Kaplan said that there had been talks with Sigurdsson over the weekend about staying.
"We all know how important Gylfi is, just as he knows how much he's valued and loved here,'' he said.
"There's been interest in him before -- there were some pretty big enquiries about him last summer and in the January window -- but we didn't want to sell him then and we don't want to sell him now."
Swansea chairman Huw Jenkins said three months ago that Sigurdsson -- who signed a new four-year contract last August -- was the subject of "substantial offers" during the January transfer window.
Everton have been linked with Sigurdsson for some time, but Swansea moved quickly to dismiss reports that a bid from the Toffees had been accepted.
"There has been no contact between Swansea City and Everton," a club spokesman said.
"As far as the owners, the chairman and the manager are concerned, they want to keep Swansea City's best players."
Sigurdsson falls into that category after an outstanding year which last week saw him named Swansea's player of the season.
After winning the award for the second successive campaign, Sigurdsson said he was happy at Swansea and would only leave the Liberty Stadium if the club wanted to sell him.
"I signed a new contract in the summer and I've got three years left," he said. "So it's down to the club if they want to sell me. But I was very happy when I was on loan here and then again in the last three years.
"I'm not trying to leave, I'm not desperate to go or anything."
However, former Iceland teammate Eidur Gudjohnsen believes Sigurdsson could be tempted by a move if a big club comes in for him this summer.
"Gylfi has had a really good season,'' former Barcelona and Chelsea player Gudjohnsen said. "He's obviously been one of the most important players in keeping Swansea in the Premier League.
"He's got tremendous quality, but he can still improve on certain things whether he stays or go.
"But he's come to an age where he might want to try his luck at a bigger club or even European football.
"It's all down to him. If he's happy where he is, he should stay.''
Sigurdsson has scored 37 goals in 131 appearances during two highly successful spells at Swansea.
He had a loan stint at Swansea in 2012 and returned in 2014 after a difficult two-year stay at Tottenham in which he completed 90 minutes in only nine of his 58 league games.