Since the transfer window opened Everton have been linked with Robert Earnshaw, Andy Johnson, Paul Dickov as well as Trundle, who has been prolific for the Welsh team this year.
Asked if Trundle was on the verge of becoming an Everton player, Swans chairman Huw Jenkins insisted, "It's impossible, as things stand. Lee is our player, is contracted to us for another 18 months and, until such time as a club come in with an offer for us to consider or refuse, there is no issue here.
"Only last week, I spoke to his agent, who told me that he fully expects Lee to sign a new contract with us this week. We remain hopeful that will be the case."
But Jenkins conceded, "Things do change very quickly in football."