The Blackpool winger was on the club's radar during the summer, while he also turned down a big-money move to the Swans' arch-rivals Cardiff as he was keen to remain in the North West region after just having his first child.
But the Swans have now gone back in for Ince as they attempt to give boss Michael Laudrup more options.
However, Jenkins admits the ball is firmly in the court of the Seasiders, who have themselves offered the in-demand star a new deal.
Jenkins told the Daily Mail: "Tom Ince is a talented player and he is someone we are looking at.
"We made an approach in the summer and have done again for this window, but it is up to Blackpool. He is their player.
"If and when there is a possibility for him to leave, then we would be interested."