The north London side paid £7 million [€8.3m] for Bale, and after a relatively slow start he has developed into one of the Premier League's finest players, scoring 19 league goals this season.
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The Scot told the Irish Examiner: “We were disappointed in Southampton because we were first there but they never came back to us.
“He was a left-back when we tried to sign him from Southampton.
“He reminds me a bit of when we signed Lee Sharpe. He was a six foot, gangly slim boy but all of a sudden he was built like a light-heavyweight American boxer.
“Bale is the same given the way he has developed physically in the last two years. He has matured very well.”
After a fine season, Bale recently secured all three main end-of-season awards - the PFA Players' Player and Young Player, as well as the prestigious Football Writers' Award.
And the Scot admits the player he previously tried to sign has deserved his accolades, despite strong competition from United forward Robin van Persie.
“You can’t dispute it,” he said. “Some of the goals Bale has scored this year have been fantastic.
“Robin is a little bit unlucky in that he hit a quiet spell and didn’t score at a time Bale was bashing them in from all sorts of distances.”
Despite rumours linking United with Bale and a whole host of star names, the club's incoming Chief Executive, Ed Woodard, has denied reports of any potential summer spending spree.
And after a relatively comfortable domestic campaign, Sir Alex agrees quality over quantity is required.
“We have fantastic strength in depth,” he said.
“That’s the area where we don’t want to confuse ourselves because you end up with too many players and having to try to keep them all happy. It’s happened a few times this season.
“But any time we’ve asked for money off the owners they have delivered.”