The Robins took up an option on the centre-back's contract last week to keep him at the County Ground for another season, only for Flint to hand in a transfer request on Tuesday.
That request was turned down, as was City's bid for the former Alfreton man, and head coach O'Driscoll is now weighing up his options.
"We've put in an offer that got rejected, so we're just contemplating whether we increase the offer or look elsewhere," he told BBC Radio Bristol.
"He'd be somebody we feel that would fill the right centre-half gap that seems to have been a problem since Steven Caulker left. He's a good age and someone we think we can develop further."