He rejoined first-team training upon Swansea's return from the States but he did not feature in their 0-0 draw against Southampton.
Swansea set an asking price of £50m for Sigurdsson in July after rejecting an offer worth about £40m from Leicester.
Clement said that the decision not to play Sigurdsson at St Mary's was one he made in conjunction with the player and the club.
"I think the way it's going there needs to be more than likely a compromise on both sides".More news: Iran Parliament Passes Motion to Counter US Measures
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"We are at a critical stage of this situation and hope it's going to be resolved very quickly".
Icelandic global Sigurdsson finished third in combined goals and assists amongst midfielders in the Premier League last season behind Manchester City's Kevin de Bruyne and Tottenham's Christian Eriksen.
The 27-year old was integral to Swansea retaining their Premier League status for another season, and his productive campaign saw only Kevin De Bruyne and Christian Eriksen, two of the league's chief creators, record more assists.
The Dutchman re-signed Wayne Rooney from Manchester United, while also bringing in Michael Keane, Jordan Pickford, Davy Klaassen and Sandro Ramirez.
And Swansea have also made an enquiry for their former midfielder Joe Allen, although Stoke insist the Wales worldwide is not for sale.