Giggs penned a new 12-month deal with United yesterday.
Harrison told talkSPORT: "He's passed his coaching badges and obviously now, with the new contract, there is a job waiting for him on the coaching staff at Manchester United and he deserves it.
"When I had him as a junior player he listened intently to me and the rest of the coaches. He took everything on board. It seemed as if he had a portfolio at home that he put everything down in.
"He looks after his body. He doesn't put any weight on. He really looks after himself. He doesn't go on many crazy nights out. In fact, I don't think he's had any crazy nights out because all he's interested in is playing for Manchester United's first-team."