The Icelandic midfielder has expressed his interest in staying with the Welsh side, stating that he is enjoying playing with them in the Premier League on loan form Hoffenheim
On-loan from Hoffenheim, the 22-year-old has hit the back of the net six times in 11 appearances for Brendan Rodgers' side, including the opener in their 3-0 win over Blackburn.
Sigurdsson, who is due to return to the Bundesliga side at the end of the season, has expressed his interest in staying with the Welsh club.
"I'm enjoying football here and as I've always said it’s not up to me, I've got another couple of seasons on my contract [at Hoffenheim]," he told talkSPORT.
"I'm really enjoying my football here in England and hopefully I can stay in the Premier League. It’s down to Swansea and Hoffenheim what happens."
Swansea’s manager, Brendan Rodgers, has admitted he’d love for the Iceland international to remain at the Liberty Stadium.
"Gylfi loves being here. He loves his training, he loves the work, he loves the city. So we'll see how that goes between now and the end of the season.
"I think everybody has seen his abilities and qualities since he’s come in, a goalscoring midfield player is very hard to find but that will be up to the board and the club to see what they can do."