Gylfi Sigurdsson has been heavily linked with a Swansea exit this summer
Sigurdsson has been heavily linked with a move away from Swansea after another impressive season at the Liberty Stadium.
The 27-year-old scored nine goals and provided 13 assists as he played a crucial part in Swansea avoiding relegation from the Premier League.
Swansea are determined to hold on to their prized asset, but Everton continue to be linked with the former Tottenham man.
"Gylfi has had a really good season," Gudjohnsen said of his Icelandic compatriot.
"He's obviously been one of the most important players in keeping Swansea in the Premier League.
Gylfi Sigurdsson scored nine goals to help keep Swansea in the Premier League
Gylfi Sigurdsson might want to try his luck at a bigger club
"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."
It was reported last month that Swansea had agreed a £25million transfer fee with Everton for Sigurdsson, but the Swans quickly dismissed those claims.
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And owner Steve Kaplan responded by revealing Swansea's desire to keep Sigurdsson, saying: "We all know how important Gylfi is, just as he knows how much he's valued and loved here.
"There's been interest in him before – there were some pretty big enquiries about him last summer and in the January window – but we didn't want to sell him then and we don't want to sell him now."
Sigurdsson recently admitted that he is happy at Swansea and would only leave the south Wales outfit if the club wanted to sell him.
"I signed a new contract in the summer and I've got three years left," Sigurdsson. "So it's down to the club if they want to sell me.
"But I was very happy when I was on loan here and then again in the last three years. I'm not trying to leave, I'm not desperate to go or anything."