A source told the newspaper: "Robbie quit a few weeks ago. He had been lined up to perform solo material and it was hoped he would sing with Take That.
“However, just as rehearsals were kicking off, he said there was an unfortunate clash of dates."
Other artists rumoured to be performing at the closing ceremony include George Michael, The Who, Emeli Sande and Take That.
However, a spokeswoman for London 2012 has said: “We want our ceremonies to be a surprise. We’ve kept all acts that might be taking part under wraps.
"There’s a lot of speculation flying about, but we’re not commenting on it.”
Last week, Williams shared his father-to-be joy with fans by posting a picture of his pregnant wife's baby bump online.
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Robbie tweeted the picture excited about his wife's bulging belly
The Angels hitmaker snapped Ayda at their LA home while she posed with her bulging belly.
He wrote "My two girls" on a message accompanying the photo.
Williams announced that his wife of almost two years was pregnant in March, later revealing that they were having a girl.
Celebrities Carry The Olympic Flame
(01 of08)
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David Beckham with the torch during the ceremony to mark the arrival of the Olympic flame, at RNAS Culdrose, Cornwall.Picture date: Friday May 18, 2012. Photo credit should read: Tim Ireland/PA Wire
(02 of08)
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(03 of08)
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Torchbearer 106 Matt Bellamy, Dominic Howard and Christopher Wolstenholme, MUSE, carry the Olympic flame on the leg between Torquay and Teignmouth.
(04 of08)
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The Black Eyed Peas star was cheered on by thousands of people as he ran through Taunton carrying the flame. The US-born music producer was a surprise addition to the line-up on day three of the relay. See PA story OLYMPICS Torch. Photo credit should read: Tim Ireland/PA Wire
(05 of08)
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Torchbearer 084 Yves Didier Drogba carries the Olympic Flame on the leg between Royal Wootton Bassett and Swindon.
(06 of08)
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Zara Phillips carries the Olympic Flame at the end of day 5 at Cheltenham Racecourse
(07 of08)
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Matt Smith carrying the Olympic Flame on the Torch Relay leg through Cardiff.
(08 of08)
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Radio One DJ Chris Moyles carries the Olympic Flame on the Torch Relay leg between Aberystwyth and Tre Taliesin.