Jenkins spoke to local media, and confirmed the rumours linking Abraham to South Wales.
Abraham was on loan at Bristol City last season from Chelsea, where he scored 26 goals in the EFL Championship.
What did Jenkins say?
"He's a young and up and coming player we are interested in," Jenkins said, “Tammy does not have Premier League experience, but we are interested.”
"Paul knows him from Chelsea. If you look at the options which have been publicised, (they are) Brighton, Newcastle and ourselves, so it is left to Tammy and his family to decide where he wants to go next."
Jenkins continued to say that Swansea’s main targets for this summer are “a central midfielder and a second striker.”
Would Abraham be a good fit for Swansea?
It would be an interesting move, as Swansea already have Fernando Llorente, Borja Baston, Jordan Ayew and Oliver McBurnie on their books.
While Abraham does seem ready for Premier League football, it is unclear whether he would be able to start regularly for Swansea.
Llorente is the undisputed number one striker, but towards the end of the season manager Paul Clement favoured a diamond system which saw Ayew partner Llorente up front.
Ayew was able to run the channels and do a lot of the off-the-ball work which freed Llorente’s game up, and the Spaniard was then able to finish the season with 15 Premier League goals.
Perhaps Clement believes Abraham can work alongside Llorente, but it does seem odd that the club haven’t gone for a player of Ayew’s ilk, as two big men up front together rarely work out.
Swansea do however face stern competition from Newcastle United and Brighton for Abraham’s services, which would almost definitely be on loan rather than a permanent move.