Beckham had stint on-loan at Preston North End as a teenager.
Harrison recalled to the Mail on Sunday: "Although Preston's team included future United boss David Moyes, it was a more celebrated man who helped Beckham's self-belief.
"Sir Tom Finney, one of the greatest English players of all time, was a Preston legend and still watched all of their matches,' said Harrison. 'After one game, he took David aside and told him what a great prospect he was, how he thought he was a really good player.
"When David came back to United and told me about that, he was glowing that someone like Tom Finney had done something like that. I do believe it made a difference and the rest is history."