The Swans were linked with Ince last summer and are known to be interested in securing his services this month with wingers Pablo Hernandez, Nathan Dyer and Roland Lamah all currently sidelined by injury.
Jenkins admits Ince fits the profile of player Swansea want to add to their squad, but played down suggestions a deal is near.
"Looking at young British players, Tom is one of them and he performs well with the England Under-21s," he told talkSPORT.
"At our club, at our level, we always look for young players we can possibly add to the squad but whether we get any further with Tom Ince or other players remains to be seen.
"At the moment it is pure speculation, but young players are always great to bring in, to see their careers develop, and we feel our club is right for that."
Swansea are also interested in bringing in another striker, with a loan move for Liverpool's Iago Aspas a possibility, but Jenkins does not expect a flurry of January activity from the Welsh club.
"At Swansea we try our best to do our business in the summer and to make sure our squad is more or less right," he said.
"There are times now and again when bringing in the odd player in January can boost morale, boost the team and get results and there's no doubt there are going to be a few clubs that do that before the window ends."