Sigurdsson, 22, joined Swansea from Hoffenheim on loan in January and has impressed since arriving at the Liberty Stadium.
The Iceland international has helped the Swans move up to eighth, with his brace at Fulham on Saturday taking his tally to five Premier League goals in nine matches.
Allen has been hugely impressed with Sigurdsson's form and is hopeful he will be playing for the Welsh side in the 2012-13 season.
"Gylfi has slotted in better than anyone I've ever seen," Allen said. "Of the young players out there I don't think I've seen too many better than him.
"On Saturday he scored another two goals and, considering that's from a midfield position, that shows how good a player he really is. A goalscoring midfielder, as everyone knows, especially at this level, is like gold dust. It's a shame that he isn't our player.
"No doubt we will do everything we can to sign him and I think, if you ask him, he'd probably agree that he'd like to stay. He's with us until the end of the season and then we've got to take things from there. Keeping him is definitely one of the priorities.
"As a team we're gifted, but he really has quality. As well as that and as well as his goals, he proved that he's prepared to work for the team. He's been a really great signing for us."