After scoring 26 goals in 48 appearances during a loan spell with Bristol City, Abraham is in demand with both Newcastle United and Brighton & Hove Albion making attempts to secure a season-long loan deal.
However, Jenkins has admitted that the Swans are also keen, and hope to make use of Paul Clement, who was previously part of the backroom staff at Stamford Bridge.
Jenkins told BBC Wales Sport: "He's a young and up and coming player we are interested in. 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."