Harrison oversaw the Beckham generation in the 1990s and believes United's football is back to their best this season.
He told the Manchester Evening News: "Last year I've got to say the build-up was so slow, painfully slow but so far this season the tempo is up 30 to 40 per cent. It's brilliant that they're playing quicker, United-style football.
"In the Community Shield City couldn't get near us as we were playing our one-twos and keeping our discipline when they tried to bully us.
"We're not as good as the '99 team as yet but the style is similar with so many strikers competing for two positions and the speed of the build up.
"People have a go at Berbatov but I think he has great control and awareness and for me he's a top player.
"There is plenty of time for Fergie to get another treble but maybe not this season.
"The boss may be coming up to 70 but he will go on until he's 90.
"Daydreaming I'm thinking that with a controlling midfielder another treble is not beyond the realms of possibility.
Asked if he meant someone like Wesley Sneijder, Harrison replied: "He'll do."