Carroll joined the Hammers on a year-long loan from Liverpool last summer and a deal has been agreed between the clubs for a permanent move.
His future has yet to be confirmed as other teams could still be interested but Liverpool manager Brendan Rodgers recently declared that he expected the issue to be resolved quickly.
Cole, who made the move from Anfield to Upton Park in January, feels Carroll should follow his example and sign a permanent deal with West Ham.
The midfielder thinks Carroll can flourish if he stays at the club and be one of the most prolific forwards in the Premier League next season.
"We play to suit him. We play around him," Cole said.
"We try to get good quality balls into the box for him, and that is going to be valuable.
"If I was him, I'd be wanting to stay at West Ham. The lads love him and the fans have taken to him.
"If he keeps himself fit he can get 20 to 30 goals next season."