The 27-year-old - who scored nine Premier League goals last season - did not travel on his side's pre-season tour of the United States, but Clement said Sigurdsson has not asked to leave the club.
"It's not something that we want [or] will be allowing to drag on until the [transfer] deadline," said Clement.
"The deadline I want it to be is imminently for everyone involved at Swansea and Gylfi included. I'm not going to put an actual day on it, but imminently means in the very near future.
"It was the best decision for everybody involved that he wouldn't take part in games at this point, but as I said recently we want a resolution to this situation soon.
"He hasn't said that [he wants to leave]. Gylfi is a player with Swansea, he has three years left on his contract, he's a very good player, we rate him very highly, we want him to stay. But at the same time if another club wants him they have to play what this club feels is the right valuation for the player.
"With either situation, assuming it's done in the right way in the right time, it's going to be a win-win for us as a club because either we get the valuation we want and we can reinvest and improve the team, or we get to keep a very good player."
Without Sigurdsson, Swansea won 2-0 at Birmingham thanks to second-half goals from Tammy Abraham and Leroy Fer.