Harrison helped guide Neville through United's youth ranks says the Reds have a long-term successor for the club skipper.
"If Gary stays clear of injuries then I see him playing past his mid-30s," Harrison told the Manchester Evening News. "It's going to be a big battle for Danny, but at least the manager knows he has someone there with the potential and character to challenge Gary."
In years to come, Harrison believes Simpson has the attributes to make the grade at Old Trafford.
"He is very similar to Gary in attitude," added Eric. "Gary wasn't as naturally talented or technically gifted as his contemporaries like David Beckham and Paul Scholes, but he was captain at 16 because he was made of the right stuff. He worked tirelessly on his game, grafting to become better technically and he succeeded by hard work.
"Danny is the same. He was a decent player as a young kid but not technically the best. But he listens, learns and it sinks in with him. His improvement has been tremendous. I don't know whether the coaches at United had question marks over him but when you see a young player work hard, take things on board and progress like Danny has you tick his box."