Rooney says he went to see Ferguson, who was United manager for 26 years, after being dropped in 2013.
"It's not just me who's had a fall-out with him," added the forward, 29, in Rooney - The Man Behind The Goals, to be shown on BBC One on 5 October.
"I don't know what happened or why that came out that way."
The England captain added: "I went in to see him and just said if you're not going to play me it might be better I moved on - then all of a sudden it's all over the press I put in a transfer request, which I never did."
Rooney did ask to leave United in October 2010 when the former Everton player pulled out of contract talks, saying he had not received "any of the assurances I was seeking about the future squad".
Ferguson said at the time he was "dumbfounded" by Rooney's desire to leave but, 48 hours later, Rooney signed a new five-year deal.
United went on to win the title that season, and Rooney later said staying at the club was the best decision of his career.
Rooney served Ferguson for nine years, and the Liverpool-born player says that despite the rift in 2013, Ferguson was "the best manager of all time".
"He was the reason why I wanted to join Manchester United, to work with him," added Rooney on how hard it was to leave boyhood heroes Everton for United in 2004.
"For him to be interested in me and want me to come and play under him, there was nowhere else I was going to go."