The Championship side is set to be taken over by a consortium that is cash rich.
The ambitious new owners would want a young and energetic manager who could ultimately get the team up to the Premier League.
And if he does take the job, Terry wants to take Cole, who is working as an academy coach at Chelsea, with him.
At the moment, Wayne Rooney is player-coach at Derby until they can find a permanent man for the job.
Rooney does want the position as well, but it is unclear if he is being considered by the new owners.