Rooney indicated he wanted to leave United in a statement issued in September 2010.
The England international later performed a U-turn and signed a new five-year contract with the Red Devils.
In his latest autobiography, which is being serialised by the Daily Mirror, he recalls: "In September 2010, my ankle puts me on the sidelines.
"I get frustrated with myself, my game, my injury, and everything around me.
"I'm stuck in a cycle of bad form but I can't get out of it.
"And that's when I make the biggest mistake of my football career.
"In October, I release a statement which publicly questions my happiness at Old Trafford. Am I better off elsewhere?
"Everyone makes a fuss. There are discussions inside United to sort out the issue, people outside United chuck their opinions around, but the thing is, nobody really knows what's going on in my life.
"None of them understand where I am in my career. They don't know where my head's at.
"The only person who really knows what's going on in there is me, but even I'm not sure what I want."
He continues: "Then the manager has his say. 'Sometimes you look in a field and you see a cow and you think it's a better cow than the one you have in your own field. And it never really works that way'.
"He's saying the grass isn't always greener, and he's right.
"I like what's in my field. I'm wrong. United want the same as me: trophies, success, to be the best."