Borini has a chance of making the bench for Saturday's match at Newcastle after recovering from a dislocated shoulder.
"He had the all-clear from the surgeon and joined in during the last couple of days and it's looking really good," Marsh said of the Italian.
"He might be included on the bench at the weekend, it might be the week after.
"He's coming to the time when he can be included off the bench pretty soon.
"It's been difficult for him - he's picked up a couple of serious injuries (he also broke a foot in October) which kept him out for the majority of the season.
"We've hardly been able to use him so it will be like an extra player. We're looking forward to that."