Giggs turned 38 this week.
Harrison has no doubts now that one of his star pupils can do it.
"Ryan has the dedication, the ability, the physique and mentality to go on," Harrison told the Mancheser Evening News.
"He is a remarkable man. His pace is still good, although obviously not as electric as it used to be and he is still so fit.
"As a coach I am always looking at players to judge their fitness and one of the ways I can monitor that is by looking at them when they have gone on a lung-bursting run and have to track back to their position. You see so many players get back into position and they are out of breath. When they do that the tell-tale sign is they put their hands on their knees and pause to get their breath back. You know they are not fit.
"I have never seen Ryan with his hands on his knees. He is never out of breath it is amazing.
"Physically he can play into his 40s and he has the football brain to do it as well. I can see Giggsy as a holding central midfield player getting the ball off defenders and started moves from deep."