The 24-year-old is currently on loan from the English south-coast club with his time in Seattle set to end on June 30 - with the Cherries opting not to recall Smith during the January transfer window.
Smith has been a regular fixture at left back for the Sounders and feels his career will benefit from remaining in the MLS.
"I think it’s definitely possible for me to stay. I would like to see the season out," Smith told the Sounders Weekly.
"I think we’ve got a great group this year and I think we can do some special things.
"But I haven’t heard anything personally from that side of it, but I think the clubs will be speaking soon-ish, rather than later, to kind of work out what we’re going to do."
Smith has 19 caps for the Socceroos but was left out of the recent World Cup and Asian Cup campaigns.
He has made nine appearances for the Sounders since joining in August 2018 - nabbing two assists.
Smith made a name for himself at Liverpool in 2016 before earning a move to Bournemouth later that year in search of regular first-team football.