The newly-appointed City Ground manager has claimed he would be interested in signing the West Brom striker should he become available, and wants better strength in depth
Cox has been strongly linked with a move to the City Ground in recent weeks and O'Driscoll - who joined Forest in July following the departure of Steve Cotterill - revealed that he would like to bring a player of the Irishman's calibre to the club.
O'Driscoll told BBC Sport: "He is a West Brom player and is under contract.
"But he's a player who has scored a lot of goals in the Championship and been in the Premier League for the last two years and, if a name like that becomes available then it would attract us."
The new Championship season begins on the August 18, and although O'Driscoll has expressed pleasure at the quality within his squad, the former Doncaster Rovers boss confessed that he would still like to recruit a few more new faces before the end of the transfer window.
He added: "Our first XI is probably as good as we would like it but underneath we are still lacking a little bit of strength in depth, as a squad we are not strong enough to cope at this minute in time.
"We will need to add players but that is easier said than done. The transfer window is still open until the end of August and we are talking to a lot of people.
"That is one stage of trying to get a player in and there are many stages."