The Capital One Cup holders have reignited their interest in the winger, who netted 18 goals in the Championship last season
The Swans supremo has confirmed that the Premier League club have opened talks with the Tangerines for the second transfer window in succession to ask about the availability of the England Under-21 international, who has scored seven goals in 21 Championship appearances this season.
Ince has shone for Blackpool since joining from Liverpool in 2011, notching an impressive 18 goals last term, and the south Wales outfit are keen to try and bring the youngster to the Liberty Stadium.
"Tom Ince is a talented player and he is someone we are looking at," Jenkins told the Daily Mail.
"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."
Swansea had also been linked with a move for Liverpool's Sterling, who could soon become surplus to requirements should the Reds sign Basel's Mohammed Salah, but Jenkins ruled out a bid, adding: "It's not correct that we are trying to sign Raheem Sterling."