The 32-year-old Londoner returned to Upton Park on a free transfer in January 2013 after a disappointing spell at Liverpool,
However, Cole started only six Premier League games for Sam Allardyce's side this season and is now on the lookout for a new club after his 18-month deal came to an end.
He 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, who started his career at West Ham, has been linked with a move to Championship side Brighton and Hove Albion.
He boasts 56 caps for England, but last represented his country in 2010.
'Mourinho called and said, "You want to play for me?" I said, "Yes sir". He replied, ‘I'll see you in Milan tomorrow" then put the phone down - I signed for Inter the next day': How Jose Mourinho easily persuaded Premier League star to make Serie A move
‘If I score only one time, I’ll go to Southampton. If I score two times, I’ll go to Leeds. If I score three times, I’ll stay’ Liverpool’s Cody Gakpo on learning the game and almost joining Leeds United
