Sky Sports revealed on Tuesday that the Swans had joined arch-rivals Cardiff City in the hunt for Ince's signature.
That interest has now been confirmed, but it appears unlikely that Ince will be heading to the Liberty Stadium.
Swansea are prepared to spend big if required, but will not be paying over the odds for any of their summer targets.
That would appear to rule Ince out of the equation, with Blackpool having set their asking price at £8million.
"The prices that have been quoted for Tom Ince are staggering," Jenkins told talkSPORT.
"Our manager has been keen on him for a while, ever since he played for Blackpool against us.
"There's no doubt he's going to get a move this summer, but I'm not sure where he'll end up going."