The shirt, which has been worn by the likes of George Best, Bryan Robson and Cristiano Ronaldo, was left vacant after the shock retirement of Eric Cantona in 1997.
As well as handing him the captaincy, Sir Alex wanted the Irish midfielder to be given the No 7, Keane has claimed in his new autobiography, The Second Half.
"The captaincy is important, but squad numbers can have an importance. At United, '7' was the iconic number.
Manchester United greats who wore the number 7 shirt
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"When Eric Cantona left there was a debate about who was going to be the next captain. I was quite relaxed about it.
"But there was his number, too - '7'. Bryan Robson had had it before Cantona and, of course, it went back to Georgie Best.
"The manager pulled me into his office and said that he wanted me to wear the '7'.
"I said, 'No, I’m not that bothered.'
"And he said, 'I know Becks will f****** want it and I don’t want him to have it.'
"The little power battles.
"I’d had '16' since I’d signed for the club. I was comfortable with '16'. I think it might have kept me on my toes, being outside the '1' to '11'. I didn’t think that I was a number '7'.
"I said, 'Give it to Becks.'
"Becks got it, and it suited him - and Cantona. Ronaldo had it after Becks."
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