The Italian has been out with a dislocated shoulder, but could return this term, while Martin Kelly will not be rushed back
Italian international Borini sustained the injury against Swansea last month, but Driscoll is optimistic that the 21-year-old's recovery from surgery is ahead of schedule.
"Fabio Borini was outside for the first time today, so he's starting that progression - passing balls, running and doing ball work," Driscoll told the club's official website. "He's due to be probably another six weeks from this point on.
"The injury he's had is normally eight to 12 weeks. He's quite a quick rehabilitator.
"At the moment, it's looking pretty positive for Fabio that he could be back ahead of schedule and maybe make the end of the season."
Meanwhile, defender Martin Kelly will not be risked this term as he continues his rehabilitation from a serious knee injury.
Kelly ruptured the anterior cruciate ligament in his right knee during September's game against Manchester United but Driscoll says the defender should look no further than the club and national team captain for inspiration during his recovery.
"Martin is doing extremely well; he's probably at the late stage of his rehab," Driscoll added.
"Martin should look at what Steven Gerrard has achieved this season; people would never have considered that he would be available for a full campaign.
"He should take great hope from that and know that if he continues to work and continues his professionalism, hopefully the future is bright. We hope to give him every chance.
"We'll probably look to prioritise getting him back for pre-season 110 per cent fit - 10% fitter, stronger and quicker, more powerful and agile than he was previously.
"He'll probably be in a position where it will be tempting to put him into games again this season. But it will show class and quality if we make sure that he's in a very strong position so he can fly next season.
"He's someone who has definitely benefited from the collaboration of the whole medical department. It's been a really great team effort, where maybe a dozen medical staff members have come together and collaborated.
"We like to encourage the whole department to have an opinion and that helps us come together and guide the player in the right direction.
"Martin has almost been a showcase for the quality of our medical science department. He's getting the best of all our staff and it's going very well."