Rooney denies that he put in a transfer request just before Ferguson retired in May 2013 but admits that he broached the possibility of leaving the club he had joined from Everton nine years earlier.
"I went in to see him and just said, 'If you are not going to play me, it might be better for me to move on'," Rooney said.
"Then, all of a sudden, it was all over the press that I had put a transfer request in, which I never did."
Three years earlier Rooney did request a transfer and questioned the club's ambition.
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"Wayne let himself down," former team-mate Gary Neville told the programme of that incident. "Me and Ryan Giggs had a word and he apologised the next day."
Talking about his international career, the current England captain admits that he should not have agreed to go to the 2006 World Cup under Sven Goran Eriksson after breaking his foot.
"It was touch-and-go as to whether I would be fit," he said. "And then Sven put me in the squad.
"Looking back, I probably would have sat out the World Cup. It was a big ask to get fit after six weeks out. I was never going to have that match sharpness."
His performances at two World Cups have been one of the disappointments of Rooney's career, which he suggests may stem from "putting too much pressure on myself".
Insights into his personal life include an admission that "having children has calmed me down a bit" and that he was determined those children should be born in his native Liverpool rather than Manchester.
Other contributors to the hour-long programme include Cristiano Ronaldo, Zlatan Ibrahimovic, Steven Gerrard, Frank Lampard and Ryan Giggs.
It is presented by Gary Lineker, whose 48 goals for England have been beaten only by Bobby Charlton's 49 and now Rooney's 50.
Rooney hopes to add to that total when England, who have already qualified for Euro 2016, play their remaining group matches shortly, against Estonia and Lithuania.
(Reporting by Steve Tongue; editing by Sudipto Ganguly)
