Manager Slaven Bilic revealed a lack of game-time was the only reason behind the 33-year-old's departure.
A switch to the Championship looks most likely, with Bolton (6/1), QPR (8/1) and Cardiff (14/1) all thought to be in the running.
But Sunderland remain contenders in what would be a controversial move.
Nolan spent nearly three years at fierce rivals Newcastle after Sam Allardyce brought him to Tyneside from Bolton.
Allardyce then took him to the Hammers and news of a potential move to Wearside might also fuel speculation that Allardyce is set to take the reins at the Stadium of Light.
Current boss Dick Advocaat remains under pressure, with Allardyce thought to be a likely successor if the Dutchman goes.
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