The Owls are desperate to add to their strikeforce, especially with former Iron loanee Steve MacLean out for most of the season through injury.
Trundle is a long-term target for Wednesday boss Paul Sturrock, but Swansea chairman Huw Jenkins says the club will not be letting their star player go.
He said: "We are trying to build a squad capable of taking the club forward, and letting Lee go would not help that cause."