The charity’s founder Camila Batmanghelidjh had said the offer of funding was reversed after Scotland Yard announced their child abuse unit was investigating the charity.
But a source close to Mr Roden has denied the allegation, and said he would still be prepared to support the charity.
The source said: “At no point did Mr Roden withdraw his offer of funding.”
Mr Roden is the chairman of hedge fund Lansdowne Partners and has been a long-term donor to the charity.
Kids Company chairman Alan Yentob has said that it was the charity who refused the money.
On Thursday night he told Channel 4 News: “Let me be fair to those incredibly generous philanthropists – we told them we cannot accept your money because it is not right… because we know that with these allegations around we will not be able to fund raise.”
Last week it was hoped that £3m could be raised from private donors, matching the funding from Whitehall.
Channel 4 News understands that if enough private donors would not come forward, Mr Roden was prepared to make up the shortfall – and even prepared to pay the full £3m if necessary.
However, hours after the offer was made allegations of sexual abuse were made and the board of trustees refused the money offered by their millionaire backers.
The claims by Mr Yentob and Mr Roden’s camp come in stark contrast to Ms Batmanghelidjh who told the BBC that her charity faced a cash crisis after a philanthropist had panicked and withdrawn his financial support after hearing of the police investigation.