The Capital One Cup winner is keeping tabs on the England Under-21 international, while it remains hopeful of striking a deal for forwards Bafetimbi Gomis and Wilfried Bony.
Michael Laudrup is looking to strengthen his squad further having already brought in Jose Canas and Jordi Amat from Real Betis and Espanyol respectively, and secured the loan signing of Jonathan De Guzman.
Reds midfielder Shelvey has emerged as the Swans' latest target with the 21-year-old thought to be valued at around 6 million euros, and Jenkins has admitted the club have scouted the former Charlton player.
Jenkins told the South Wales Evening Post: "He is a young player we went to watch last year, but it hasn't gone any further than that."
Wilfried Bony and Bafetimbi Gomis are two other transfer targets Swansea has set its sights on, and Jenkins insists negotiations are ongoing and remains hopeful the signings will happen.
"We are still talking on a number of fronts to try to get the right players on the right deals for Swansea City," he continued.
"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."
He added, "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."