The Daily Star says Taylor has triggered a £1m release clause in his contract which is set to clinch him a move to Newcastle United.
As far as Rodgers is concerned, it's good riddance to Taylor, who missed out on the Swans' play-off final win over Reading through suspension.
"There will be no player at this club who does not want to be here," he said.
"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."
Taylor has spoken to Swans chairman Huw Jenkins but Rodgers claims the defender has blanked him since news broke that he could be on his way.
"Newcastle have put a bid in which gives him permission to talk to them," added Rodgers. "I've tried to ring Neil several times but haven't heard back from him, so I'm just waiting on that."