But O'Driscoll is keen to put the record straight on the issue and believes people have jumped to conclusions regarding Saints' interest in Stock.
O'Driscoll says he has not been contacted by the League One club regarding the former Bournemouth man and believes it is just a 'ruse'.
"He's a Southampton lad so the media put two and two and two and two together, and come up with whatever they want to," O'Driscoll told the club's official website.
"To me this is just a ruse to sell newspapers with no one contacting me about it to add the Rovers side of the issue.
"I believe Alan Pardew was asked by a journalist after the game about Brian Stock and his quote was that he felt that Doncaster's valuation of their skipper would not match theirs. My valuation of their skipper would be different to theirs, as would my valuation of Robinho if asked, and it annoys me that people jump to conclusions.
"I know the industry is full of rumour and speculation, but if you write something, you talk to the people involved with a direct quote from me or from Alan; not just write stuff that upsets people such as players.
"To put the record straight, I have had no contact with anyone over Brian or had any offers."
Coca Cola Ch'ship Promotion 09/10 Win Outright: Doncaster 20/1