The midfielder, 30, a free agent having left Portsmouth last month, has been given the opportunity to prove his fitness in an Under-21 match at Millwall on Tuesday.
"Brian is someone I've tried to sign before at Crawley but it wasn't such an attractive prospect as joining Bristol City," O'Driscoll said.
"He's not long had a hernia operation so we need to do some due diligence and see where his fitness is.
"He'd be a great asset for us, a great personality to have in the dressing room, but we'll have to see whether we offer him anything."
Howard, who has played for the likes of Barnsley and Swindon, began the season with Portsmouth and continued to sign month-long deals with the npower League One strugglers until his contract was cancelled in January.