The former England international returned to Upton Park for a second spell in January 2013 after initially quitting the club to sign for Chelsea in 2003.
However, the 32-year-old has only made 13 Premier League starts since and has hinted that, with his career winding down, he needs to move in the summer to secure more regular football in his preferred position.
When asked on Sky Sports News if he would be staying at Upton Park, he replied: "At the moment it's probably looking unlikely. If I could stay and play then that would be ideal but that doesn't look like I'm the manager's first choice.
"I'm being used here and there and sparingly. But at my age and where I am in my career I want to enjoy my football. I love competing and just I want to play. If you look at the small amount of time I've played on the pitch I think I've performed reasonably well.
"I'll be looking next year to play in a more central role. Being a winger in the past 10-11-12 years you lose a bit of patience, you want to come inside. Playing central will be something I will be looking for in my next club or if I stay at West Ham. So we will sit down in a few weeks, I imagine, and get a plan for next year."
Former England international Cole has been capped 56 times by the Three Lions.