Fletcher was a highly rated youngster and Ferguson was desperate to seal his fellow Scot's signature early on.
The Red Devils made contact with Fletcher early, but the midfielder didn't make an immediate decision and it left Fergie sweating.
"I nearly signed for Newcastle United," Fletcher told the Lockdown Tactics podcast.
"I had been going to United from the age of 12 and Newcastle at this point were the second-biggest team. Everyone is telling you, 'look at all of these great Man United midfielders you'll never get in the team, difficult to break through, Newcastle is closer to home.'
"I really enjoyed it there, great club, Sir Alex Ferguson at this point  was going to retire."
The news got back to Old Trafford and Ferguson was less than thrilled - so he decided to sort it out himself.
"So the word gets back to Sir Alex and he phoned the house one night and my sister picked up the phone. 'Here, Darren. It's for you'. It's just the boss going absolutely mental.
"I'm 15, just chalk-white and he's f'ing and giving it to me down the phone. My mum sees me and grabs the phone and listens for a few seconds and goes, 'don't speak to my son like that ever again', and slams the phone down.
"So the next minute the phone rings up again, it's Sir Alex: 'really sorry, Mrs Fletcher but we really like your son, I'm coming up on the next flight to Edinburgh'.
'My mum's looking around the house thinking, 'I've not done the housework, I've got loads of washing'. She goes, 'no you're not, they'll come down and see you'."
It's no secret Ferguson wanted United to be the best and they were for most of his 26 years in charge.
Fletcher spent 12 years at United and he went on to explain the impact that conversation had on his career.
He is now back at United as technical director and works closely with Ole Gunnar Solskjaer.
"To be honest, deep down, I could tell my dad recognised that going to Man United was the best thing for me, Sir Alex doing that. Anyway it got sorted, you go to Manchester United at 15 and it's the best decision I've ever made and the manager, what an influence he was on my career."
Fletcher was struck down with ulcerative colitis in 2011 which had an impact on his final few seasons in Manchester.
Despite this, Ferguson was always there for him and his family which the 37-year-old will always appreciate.
"He's another one who was there for me every step of the way. He was the one who gave me my debut in the first team, seen me through injuries as a young kid, and more so than anything, that time when I was out ill, looking after me,' Fletcher explained.
"I was worried about my contract and he was like, 'do not worry about that, you've got to get yourself right for your family, you've got to get yourself right for the rest of your life, don't worry about football."
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