The Australia international joined Seattle in August last year on a season-long loan deal until June.
Asked about his future, Smith told the Sounders website: “I don't have any updates at the moment. I am sure everyone's anxious – me as well because I'd like to stay out here. I am really enjoying my time here.
“I am grateful to be here and playing with such a great team. Hopefully time will tell, hopefully I will stay."