The Portuguese coach made the revelation in a new Netflix documentary charting his career, explaining that he had reached an agreement to succeed Ferguson after leaving Real Madrid.
"When I left Real Madrid, I signed with Manchester United to go to Manchester United after Sir Alex," Mourinho said.
The opportunity came after Ferguson announced his retirement at the end of the 2012-13 season, bringing an extraordinary 26-year reign at Old Trafford to an end.
"He was offered the job, yes," Ferguson said. "I sat him down and explained the situation. And as far as I was concerned, he was accepting. And then within hours, it changed."
Mourinho's change of heart was driven by his desire to return to Chelsea, where he had established himself as a club favourite during his first spell.
"I was, of course, very flattered, because Manchester United has an incredible appeal," Mourinho said.
"But one thing is love for football, another thing is love for a certain club. I think this is more powerful than love for football and fundamentally, after Real Madrid, I needed to feel that I'm loved."
Ferguson revealed that Mourinho personally called him to explain his decision, with the Portuguese reportedly emotional during the conversation.
"Early evening he phoned me and he was crying and he says, ‘Alex, I can't take it. I've given my word to Chelsea and I'm not going to break my word,'" Ferguson said.
"The reason he gave to me I could understand, but I was disappointed."
Mourinho subsequently returned to Stamford Bridge in 2013, while United appointed David Moyes as Ferguson's successor. Moyes' tenure lasted only 10 months before he was dismissed after a disappointing campaign.
Mourinho later acknowledged that missing the opportunity to follow Ferguson was a dramatic moment in his career, but insisted he had no regrets.
"For me to lose the chance to be the coach to succeed Sir Alex Ferguson was dramatic," he said. "But I don't regret it because it was a decision that I made with my heart."
United eventually appointed Mourinho in 2016, three years after he had initially agreed to take the job. He succeeded Louis van Gaal and delivered the Europa League, League Cup and Community Shield during a two-and-a-half-year spell before leaving the club in December 2018.
