The former Tottenham Hotspur and Fulham striker, the only player to score in three World Cups for the United States, underwent medical checks last week.
"Dempsey has been cleared to return to training...but he's not been medically cleared to play," general manager Garth Lagerwey told the club website (www.soundersfc.com).
"When Clint feels better and the doctors consider it safe, then we will consider his return to play. You can't just say, 'Clint's important to us', you have to mean it and that means Clint's health comes first."
The 33-year-old has scored seven goals in 12 MLS games this season but has not featured in the league since netting twice in Seattle's 3-1 win over the Portland Timbers on Aug. 22.
Dempsey joined Fulham in 2007 and scored 57 goals in 218 Premier League appearances for them.
He spent the 2012-13 campaign at Spurs and played 43 matches in all competitions, netting 12 goals.
Dempsey has scored 52 goals in 131 appearances for the U.S. He was on target three times as his country reached the semi-finals of this year's Centenary Copa America.
(Reporting by Ian Rodricks in Bengaluru; Editing by Tony Jimenez)
