Cole, 32, returned to his first club on an 18-month deal in January 2013 but played only a bit-part role in the season just concluded.
He moves on having not started a game in the Barclays Premier League since scoring in the 3-3 draw with West Brom last December.
Cole is not ready to retire and told talkSPORT: "I'm a free agent now and I'm looking for a new club.
"My relationship with West Ham is great, but obviously it didn't work towards the end of this season. I didn't play enough.
"So I'm just going to take my time over the summer and find the right fit.
"At this stage of my career finances are not important for me, I want to enjoy my football, I want to compete and I just want to play more."
Cole, a West Ham academy product, was regarded as one of the most gifted players of his generation.
He left for Chelsea in 2003 and won three Premier League titles during a spell when he became an England regular but injuries saw him fall down the pecking order at Stamford Bridge.
A move to Liverpool in 2010 failed to reignite his career but he enjoyed a successful loan spell with Lille before returning to Upton Park.
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- Barclays Premier League