England international Carroll joined the Hammers on season-long loan last month after being told that he was surplus to requirements at parent club Liverpool.
However, despite seeing his place in the starting lineup come under threat from Carroll's presence, Cole has insisted that he will use the competition to make him a "better player".
"Every year, you have to have people challenging for places because it is healthy for the club," he told the club's official website.
"It's better to always be on your toes and I welcome a challenge like Andy Carroll because he is one of the best target men around in the Premier League and it's just going to reinvigorate me to be a better player."
Recent reports have claimed that Carroll will be out for six weeks with a hamstring injury.