The 28-year-old has been linked with a move to Fulham, while Turkish club Galatasaray are also reported admirers.
However, the England international has revealed that he would like to continue his career with the Hammers beyond the current campaign.
"I told everybody at the start of the season, I'm there for the whole season," he told Sky Sports News. "Next season I want to be here at West Ham again. I'm not looking for a move.
"Obviously when you're connected to other teams it's a bit unsettling and unnerving sometimes but I know the chairman has got 100% faith in me and he wants me to do well, the manager as well.
"I've got no reason to move at the moment."
Cole joined West Ham from Chelsea in 2006.