Having come out of retirement last season, 23-year-old Hutchinson signed a contract with the Blues last December.
However, his game time has been limited at Stamford Bridge and as a result manager Roberto Di Matteo is believed to be willing to loan the centre-back out to a club in the Championship.
"When you talk about good characters, he is certainly one of those. He is somebody who is on our radar," O'Driscoll told the Nottingham Evening Post. "He is a Chelsea player and they have to decide what they want to do with him this season.
"He is very highly thought of at Chelsea. That bodes well, if you can get a player of that quality into the club. It would be a loan signing if we could do it.
"We are trying to see where the land lies with him and to make something happen, if we can. He is certainly somebody we are interested in signing but we will have to see what happens."
Hutchinson made two appearances for Chelsea towards the end of the last campaign.