The USA star had been out since the end of August after the discovery of the problem.
He missed USA’s last two FIFA World Cup qualifying wins.
“He has had a procedure to address some of the issues [of his irregular heartbeat],” Sounder general manager Garth Lagerwey said.
“We’re not at liberty to discuss anything further from medical perspective. We’re cautiously optimistic he could return this season.”
Lagerwey also confirmed there is no timetable for Dempsey’s return to action.
“Dempsey has been cleared to return to training, to exercise, but he’s not been medically cleared to play yet. No timetable,” he said.
“When Clint feels better and the doctors consider it safe, then we will consider his return to play.”
According to the Sounders GM, Dempsey remains in good spirits as he battles back into shape.
“Clint has seemed really positive and cheerful,” Lagerwey said.
“He’s been out here jogging and working, and he has a good attitude about it. Having watched interactions out on the field today, Clint’s return was really positive and happy for the rest of the players.”