Forrest has not played since the start of the month, after he sustained an injury while with the Scotland national team.
However, the 24-year-old has returned to training with Celtic this week, and he has suffered no repercussions.
It leaves Deila with almost a full squad from which to select, but the Norwegian boss did state that Saidy Janko was struggling after picking up a knock.
“Jamesy is available,” Deila said. “He has trained over the last four days which is good, and there are no other injuries, though Saidy Janko is strugging after a kick.”
Forrest's career has been plagued by injury to date, and his latest fitness issue came at a bad time, as he was in such good form.
Forrest had finally been starting to live up to his promise at Parkhead, and he will be hoping to hit the ground running when he does return to competitive action.
If the winger plays against Hearts, he will be under pressure to perform, as Celtic are keen to defend their League Cup title.
Gary Mackay-Steven has already expressed his desire to win the trophy, on the club's official website, as the Bhoys look to build on the domestic success they achieved last season.