The 27-year old was instrumental in keeping the Swans in the top flight, having scored 9 goals and provided 13 assists.
Sigurdsson has recently been linked with a move to a host of Premier League clubs including Everton and former club, Tottenham.
Speaking to Association Press Sport, Gudjohnsen said: "He's obviously been one of the most important players in keeping Swansea in the Premier League.
"He's got tremendous quality, but he can still improve on certain things whether he stays or go.
"But he's come to an age where he might want to try his luck at a bigger club or even European football.
"It's all down to him. If he's happy where he is, he should stay."