The Daily Echo says the Australian international has made just five Premier League appearances since joining the Dorset club in July 2016, the most recent of which was 18 months ago.
Any deal would see Smith link up with the Sounders on loan until June next year, although Cherries would have the option to recall the 24-year-old in January.
The MLS regular season runs from March until October, with the play-offs taking place in November and December.
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