The 27-year-old has impressed for Fulham in the last few games and originally signed a one-year deal when he joined the club from Kalmar FF in the summer.
The Cottagers hold the option to extend Elm’s deal.
“Nothing about a new deal has happened as yet, but we have got indications off Fulham that they want keep David,” Elm’s agent, Patrick Mork, told Sky Sports.
“They have shown positive indications about taking up a two-year option in his contract and I would be surprised if they didn’t.
“David would be delighted to sign a longer contract at Fulham as he is enjoying himself there.
“They have until March 31st to take up the option and if they don’t I am sure there will be other clubs who will be interested in David.
“He is getting more confident now he is playing regularly and he is happy playing under Roy Hodgson.”