The Icelander, who has scored seven goals in 15 appearances since joining on loan from Hoffenheim in January, has said he would be happy to stay with the Swans, but Jenkins knows persuading the German club to sell the 22-year-old is another matter.
He told BBC Radio Wales: "He's done a great job for us and is still only young. Our aim is to keep our best players. We've always tried to do that over the years and it will be no different with Gylfi."
He added: "The fact is when you take a player on loan, control is out of your hands. They (Hoffenheim) wouldn't commit to do a deal before we took him, which we would have loved to have done.
"But we've got to hope that his relationship now with the club, with the players and with (manager) Brendan (Rodgers) has helped him in the Premier League, and he sees us as a great option next season if he's allowed to leave his club in Germany.
"No doubt there's going to be a bit of a battle on our hands to secure his services for next season. The other thing is they (Hoffenheim) have had a change of manager as well and he's still contracted there for a couple of years."
Jenkins is also hoping Tottenham will sanction another loan deal for Stephen Caulker, who has impressed alongside Ashley Williams in central defence.
Source: PA
Source: PA