Rumours that Everton were interested in the 29-year-old have intensified since the Toffees sold Marcus Bent to Charlton for £2.5m earlier this week but Swans chairman Huw Jenkins insists Trundle is staying at the Liberty Stadium.
"We have received no bids at all for Lee Trundle (in the transfer window), there's been no correspondence with any club," he said.
"He's not for sale. We want to keep all our best players to help bring success to the club. It's totally hypothetical. Until we get something in writing there is nothing to consider.
"It's just media speculation as Everton have just sold a player. That's all it is."