The 21-year-old has not played since picking up a hamstring injury in March's 2-0 UEFA Champions League last-16 second leg defeat to Juventus.
But Matthews has been back in training and he hopes to return to action, starting against St Johnstone at Celtic Park on Saturday.
"I've trained the last couple of days so hopefully I can keep fit and not get a recurrence of injury and I'll be fit for the weekend, hopefully," he told Sky Sports News.
Celtic will play Hibernian in the Scottish Cup Final on 26th May and Matthews would love to help Neil Lennon's side to their first Double success since 2007, with the SPL title already in the bag.
"It's been a great season so far so hopefully we can finish on a high and get the win we need," he said.
"We know it's going to be a tough game but we know what we've got to do to get the win so hopefully we can do it.
"It'll be brilliant (to do the double). We haven't done it for a few years and with the Champions League win as well, if we can top it off with the cup, we've had a great season, we know that.
"So we'll just fully focus on what we need to do on that day and we can beat Hibs hopefully."