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The England Under-21 international midfielder 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."