The 31-year-old former Stoke and Burnley man, who left Southampton at the end of last season, has been training with Rovers over the summer.
He has also appeared in their pre-season friendlies against West Brom and Sheffield Wednesday and O'Driscoll is keen to add him to his ranks on a permanent basis.
"We will chat to his representatives and decide what we are going to do," he said. "He hasn't done anything wrong. I think he has got one or two things in the pipeline but the season is a week away.
"The thing with 'things in the pipeline' is that they are fine but you need some concrete offer. I can envisage us making some kind of deal - whether it gets accepted, I'm not too sure."