The South Wales club have not even tried to hide the fact that they are looking to flush out interest in the teenager so that they can receive a bigger fee.
But Taylor is sold on a move to Newcastle and Toon chiefs believe it will happen, says the Sunday Sun.
Swansea boss Brendan Rogers said on Friday: "There will be no player at this club who does not want to be here.
"If a player decides they want to speak to another club, they can go, it's as simple as that. I'm only interested in those who want to play for Swansea."