West Ham and stay on beyond this winter.
The burly forward recently re-signed for the Hammers, after being released by them over the summer, on a short-term deal that expires in January.
Cole was allowed to leave Upton Park at the end of last season, and was expected to make a move to France.
However, he was unable to find a new club.
Meanwhile, West Ham boss Sam Allardyce found himself short of attacking options with Andy Carroll sidelined through injury.
Cole was invited back to train with the club and eventually proved his fitness before penning a three-month deal to solve the Londoners’ issues.
Despite the contract being a particularly short one, the 30-year-old is hopeful that he can play his way to an extension.
“If I’m doing the business, doing well and making a difference in the team, we are in good shape and the manager and the Chairmen want to keep me on, I’ll always be available and hopefully we can crack on after that,” Cole told talkSPORT.
“Of course me and the fans have been through thick and thin with this club. I’ve been here for quite a while and I know the emotions of us getting relegated and getting back up.
“It wasn’t all roses, but I will always have a special bond with the club because we’ve been through everything together. I think the fact they realise I am a fan and will always be here means I will earn their respect a second time and make a positive impact on the team.
“I’ve always wanted to prove myself and hopefully, with this second chance at West Ham, I can help the team. That’s all I want to do. I want us to stay in the top league where we deserve to stay.”
Despite possessing a questionable goalscoring record in recent years, Cole is still a fans’ favourite at West Ham.
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