Brooking was caretaker manager of the talented Hammers team that were incredibly relegated in 2003, which was captained by Cole and led to his £6.7million move to Chelsea.
The Hammers great said: “Joe has always had a soft spot for the club and been a popular figure for fans.
“Even when he scored against us before Christmas with Liverpool, he didn’t celebrate.
“It’ll be interesting to see how he comes back now he is experienced rather than an emerging star. Let’s hope we can give him a good late spell in his career as there is a lot of affinity between him and the fans.
“During my three-game spell in charge at the end of that season, I remember Joe in training. He could dribble past anyone. And sometimes you wanted him to veer his game and release the ball quicker.
“He’d beat three people and then lose the ball on the fourth attempt. And his dribbling skills didn’t have that cutting edge that they should have done.
“Then there was the issue of where to play him? Do you play him centre midfield, channel him wide or in the hole behind the main striker?
“We had a lot of injuries during his last season and he was forced to play in many different positions, which may not have been good for him.
“It’ll be interesting to see where he fits into Sam Allardyce’s system - but certainly he has the skill and experience to be a success. It’s up to him now to be the first name on the team-sheet.”