Manager Paul Clement has previously insisted Sigurdsson will only leave the club on their terms: 'He is training hard and straightaway he is at the top of all the statistics physically, ' said the Swansea boss.
Sigurdsson did play in Wednesday's pre-season loss against Barnet, and even captained the side in the second half, as he has done before in the Premier League.
That is because Swansea are reportedly using Everton's £50 million valuation of Ross Barkley as a yardstick for their own valuation of Sigurdsson.More news: GLP sold to Chinese bidder for $16b
"The fans want that, our owners would like that, but we also know that there is a business side to things".
Swansea slapped a £50million ($64 million, 56.4 million euros) price tag on him, with the Welsh club having rejected a £40m bid from 2015-16 champions Leicester. That might end up being the case with Gylfi.
"You can't say how people behave in the future, I just know the character I have worked with last season and he has come back, got his head down, working hard and I hope it continues and with us".
Sigurdsson had a fantastic season for the Swans scoring nine goals and providing 13 assists, helping his team avoid relegation to the Championship.More news: Vertu Collapses As Luxury Smartphone Market Dries Up
The Iceland worldwide is one of the Swans best players, and his future at the Liberty Stadium is under increased speculation.
That figure could now rise significantly as Sigurdsson returns to Wales to speak to Swansea chairman Huw Jenkins about his future.
Everton have courted Sigurdsson throughout the summer, and are now thought to be closing in on their ninth signing of the summer.More news: Rent-a-Center shares soar after rejecting takeover bid
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