Speaking in a new documentary series about his career, which is on Netflix from 11 August, Mourinho said: "When I left Real Madrid, I signed to go to Manchester United after Sir Alex."
Ferguson, who won 13 Premier League titles as United manager, confirmed Mourinho was "offered the job". "I sat him down and explained the situation," he added. "As far as I was concerned, he was accepting. And then, within hours, it changed."
What changed was that Mourinho felt he could not turn down a return to Chelsea, where he had won consecutive Premier League titles in 2005 and 2006.
Ferguson said: "One night, 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.' The reason he gave to me, I could understand, but I was disappointed."
Mourinho, 63, said he was "very flattered" to be offered the job of replacing Ferguson "because Manchester United has an incredible appeal".
"But one thing is love for football, another thing is love for a certain club," he explained. "I think this is more powerful than love for football and fundamentally, after Real Madrid, I needed to feel that I'm loved. For me to lose the chance to be the coach to succeed Sir Alex Ferguson was dramatic, but I don't regret [it] because it was a decision that I made with my heart."