Jones played in a variety of roles last season - all successfully.
"It is very difficult when you have the adaptability to play in a number of positions," Harrison told the Manchester Evening News.
"I think if you want to have a long, established career at a club like United at the very top level and also have a long international career, it is vital you cement one particular position.
"I think it can hinder you if you don't get that. I think Phil Neville, for instance, was hindered by it. I was Phil's youth team manager and I always played him at right-back and he was superb there for me. But his way at first-team level was blocked by his brother Gary. Phil was versatile and so had to move around and he did a very good job.
"However, I believe if he'd tied down one role then he would still be a Manchester United player now. I am 100 per cent convinced he'd still be at the club now had he been able to do that.
"When you establish yourself in one position, you build up relationships with other players around you. Like, for instance, the way Gary Neville did with David Beckham down the right wing. You fill in for the other player if he goes forward. You know what each other is going to do. It's the same if you are at centre-half or in the centre of midfield.
"But if you are only dipping in and out of those roles for short periods of time it is so much harder.
"When you get a chance to play for United, you obviously take it no matter where you are played. It is what you dream about, playing for United, so you don't complain. All the versatile players are really good lads who'll stick their hand up for a job. The manager doesn't mess them about. He has to do things for a reason and that reason is to help United. These kind of players wouldn't go banging on his office door to demand a certain position either because they respect him too much.
"But, in the long term, it can have an effect and Phil Jones faces that danger. But I have a feeling he is going to end up in one role. I'm sure it will happen."