The former midfielder retired earlier this year due to injury troubles having enjoyed a fine career at the top level.
After coming up through the ranks at United and breaking into the side under Sir Alex Ferguson, it became apparent that he would need more first-team football in 2014.
Fergie agreed to let him go with Everton and Aston Villa competing for his signature.
Cleverley ended up signing for the latter on loan - but only after already agreeing to join Everton.
That transfer fell through and resulted in an awkward conversation with Keane, who was assistant manager at Villa at the time.
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Speaking to Ben Foster on his YouTube channel, Cleverley explained all and said: "Before the Villa loan, I had been to Roy's house because we lived very close to each other.
"He sold me the Villa project, he was assistant to Paul Lambert at the time, I really liked the idea of it.
"I was also speaking to Roberto Martinez at Everton, who I had worked with [in 2010/11].
"I probably should have been a bit more transparent and said I was speaking to Everton as well.
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"Anyway, I didn't commit to Villa but I sort of said 'oh yeah, I hope we can get things done'.
Foster interjected and said: "You were c***-teasing them basically?"
Cleverley chuckled and said: "I don't want to admit to that!
"Deadline day, I basically out of respect text Roy and said I'm gonna sign for Everton.
"He has sent me back a mouthful, not happy. Anyway, the deal between United and Everton fell through. I ended up going to Villa on loan.
"The next day, I trained at Villa. He weren't there, he was with Ireland duty. So all the nervousness, I had to go through twice!
"I had to go through those ice-breakers again, but anyways, it was fine."
Cleverley spent the season on loan at Villa but he would get his wish and sign for Everton in the end, joining the following summer, turning down Villa again as they looked to make the loan permanent.