The 30-year-old United States international joined Spurs just 12 months ago when they paid Fulham over £6million for his signature.
However, his future now looks set to lie away from White Hart Lane and a move back to Major League Soccer could be in the offing.
Dempsey last played in his homeland back in 2006 when he left New England Revolution, but he could now get the chance to do so again with Seattle.
Sounders boss Sigi Schmid was coy about the Dempsey rumours when asked by local media.
"We're always interested in good players first off," he told Sports Radio KJR.
"Right now, there's really nothing to it, there's nothing to say. But we are in a position to add a Designated Player to our team before August 8th.
"I know Clint. I talked to him when he was here when he was playing against Panama. I always follow what he does and his career and what he did in MLS, but there's nothing there that I can say right now.
"We're always looking for good players. You can't really close the door on anything, but right now there's nothing that's nailed down and concrete."