The England Under-21 midfielder has been linked to a host of clubs, and now Swansea have revealed their interest.
Jenkins was quoted by the South Wales Evening Post as saying: "There is an interest there and we are talking to Liverpool."
Vitesse Arnhem forward Wilfried Bony and Lyon striker Bafetimbi Gomis have also been attracting interest from Swansea, and Jenkins confirmed talks about both players were ongoing.
"We are still talking on a number of fronts to try to get the right players on the right deals for Swansea City," Jenkins added.
"There have been continual conversations on Bafetimbi Gomis because he has been one of our main targets.
"The fact is that there are quite a lot of things which need to be sorted out at Lyon's end which are out of our control.
"We have kept the door open on that one. Similarly with Wilfried Bony, we are waiting for information.
"We are waiting for news back from his club - we are still talking to them."
Jenkins also confirmed that the club had looked at Espanyol wideman Wakaso Mubarak, with some reports claiming the 22-year-old could follow former club-mate Jordi Amat to the Liberty Stadium - after he finalised a move last week.
However, Jenkins said the club had not made an official approach, adding: "He is a young player we went to watch last year, but it hasn't gone any further than that."
It is also being reported in Holland that the Swans are poised to make a move for FC Twente's highly-rated Belgian international Nacer Chadli.