The Liverpool midfielder has one year left on his contract and, despite gaining massively in popularity this season, it is unlikely he will still be a Liverpool player at the start of next season.
The 'Welsh Pirlo' has already told reporters a couple of weeks ago that his future at Anfield dependeded upon how many first-team chances he will get and who Jurgen Klopp brings in over the summer.
“I think it has been well-documented that Joe is going to look at his future when he is finished out at Euro 2016,” Swans chairman Huw Jenkins told the South Wales Evening Post.
“Naturally, we are interested in good players like Joe who may be available this summer given that he has a year left on his contract.
“Obviously we will keep tabs on his situation and see what happens later in the summer."
With Francesco Guidolin agreeing a two-year contract to stay at the Liberty Stadium last month, he is now looking to bolster the squad ahead of the new season.