The former Chelsea, Barcelona and Bolton striker is without a club after departing Greek outfit AEK Athens in July and Sounders general manager Adrian Hanauer has confirmed they are casting an eye over him.
"This one was a little bit out of the blue. We were contacted by his representation and anytime you get a chance to look at a player of Eidur's quality and (soccer resume), you jump at it," he told the Seattle Times of the Iceland international.
"He seems like a really good guy, wants to be here and show what he can do, likes this area - has been here a couple of times to the Northwest - so we'll see.
"Obviously we got a chance to see him today and we'll get a chance throughout the week, and then we'll see from there."