Those exploits have made him a much sought-after talent and another loan deal is expected, with Newcastle and Swansea among those reported to be keen.
And the striker is now on worldwide duty with England at the Under-21 European Championships.
"If you look at the options which have been publicised, [they are] Brighton, Newcastle and ourselves".
But Abraham is now on global duty with England at the UEFA European Under-21 Championship, and is not likely to make a decision on his future until the competition is over.
On one hand, it's probably the best thing for his career to go out on loan again, get regular playing time and in this case with Swansea, play in the Premier League on a regular basis to prove himself at that level.
"We will do our best to add to the team, not take away from it, " Jenkins added. When a player does that someone will pick up on it and talk about players being wanted by other clubs in the Premier League.
"Our aim is to try and keep Gylfi and Fernando, keep our better players and to make sure we can add to Paul's [Clement] squad".
However Jenkins says it is just speculation and hopes they will stay.
But one player who seems set to leave the Liberty Stadium is Bafetimbi Gomis.
"He's a young and up and coming player we are interested in".
'Gomis (moving) to Galatasaray is possible, we have been talking, ' Jenkins said.
'The main positions we are looking for (with the way that we play) is a central midfielder and a second striker.