Celtic boss Ronny Deila says keeping his best players will take priority over acquisitions in the transfer window.
Chelsea striker Fernando Torres is understood to be set for a return to Atletico Madrid, according to Sky sources.
But O'Driscoll is interested in signing Brendan Moloney from former club Nottingham Forest during the January transfer window.
The City boss has also clarified the Ashton Gate position on transfer targets Kyle McFadzean, Matthew Bates and Mark Wilson.
O'Driscoll poured cold water on rumours he will sign Crawley Town defender McFadzean and stated that despite lengthy talks between the two clubs, any deal is now on hold until the summer at least.
But he is keen on signing Republic of Ireland defender Moloney, who played under him at the City Ground.
"We are talking to Brendan and, if he is available on a free transfer, which we are aware he is, he will be a good addition for us," said O'Driscoll.
"He can play right-back, left-back and centre half and, at 24, is the right age. He has played a lot of games in the Championship and has never let me down."
"Financially, he fits in with what the club want to do in the future and he is reliable and solid as a character."
"He has been at a club where he has not had enough games, because they have always had the ability to buy someone more expensive. If they sign someone who is more expensive, they usually play ahead of you.
"That happened with me this season. He started the season with me and I then had the opportunity to bring in someone else and Brendan had to be patient."
Former Middlesbrough defender Bates is out of contract and has been given more time to impress the new head coach. However, he remains unavailable through illness.
O'Driscoll also says former Celtic defender Wilson is likely to remain with the club for the rest of the season.