The Labour peer was giving evidence at the trial of Elaine McGonigle, a former director of the New Pyjamas Campaign set up to raise £15 million to build a new Royal Hospital for Sick Children in Edinburgh.
Mrs McGonigle, 50, who faces 13 charges of fraudulently claiming expenses, is alleged to have invoiced the organisation for the cost of dinner with the then MSP and another man, the city's sheriff court heard yesterday.
However, Lord McConnell told the court that, although he knew the fundraiser after a campaign launch in October 2009, he could not have met Mrs McGonigle for the alleged dinner on April 4, 2009, in Edinburgh, as he would have been with his family in the west of Scotland.
The former MSP had earlier outlined in court how he had been contacted by someone, possibly Mrs McGonigle - whose husband he had known at university - from the New Pyjamas Campaign.
He agreed to her request to act as an ambassador for the fundraising initiative, to help raise the funds needed through his contacts and raise publicity.
Lord McConnell explained he had "little reservation about giving help" because a nephew had been treated at the hospital after suffering serious injuries in a road accident in 2003.
Since the incident, he said that he had maintained links with the campaign organisers, the Sick Kids Friends Foundation.
He said: "I felt very, very grateful for the treatment to my nephew and I saw this as an opportunity to give something back to the hospital."
The peer said that he organised the launch of the campaign in the Scottish Parliament, when he and Mrs McGonigle dressed in pyjamas, with images appearing in the media.
Lord McConnell said the campaign organisers may have kept in touch with his office subsequently.
However, more than a year later, on August 27, 2010, Lord McConnell was contacted at the Parliament by a police officer who asked about a claim from Mrs McGonigal that she had met with him on April 4, 2009.
He said: "I checked my diary and my staff and the date that was put to me by the police was definitely not in my diary, not remembered by me and not remembered by my staff".
In his statement given to police, Lord McConnell said: "From memory I have no recollection of having dinner with Elaine McGonigle."
He told the court his diary showed there were no appointments on April 4, 2009 and that he was "pretty certain I was with my family that day".
He added that, in any case, he had travelled to Edinburgh the following day and flown to New York.
Cross-examined by defence counsel, Drew Mackenzie, the peer said that he had first heard of the New Pyjamas Campaign in 2009.
Mr Mackenzie suggested it was in fact 2008, and that someone in his position would have been aware of that.
Lord McConnell replied: "I don't think so.
"I am a non-Edinburgh resident and although I receive the Foundation newsletter I have no regular contact with the hospital".
He said he had heard that McGonigle had been suspended and when asked about the date and location of the claimed for dinner he had been "very surprised".
He said that he would have been in the west of Scotland and would have been surprised if someone had arranged dinner for a Saturday when he was with his family.
Mrs McGonigle, of Errol in Perthshire, denies making false claims for expenses.
The claims for meetings, food and travel, were said to have been made between September 22, 2008, and March 5, 2010. The alleged frauds are said to have totalled £1855.
The other man claimed to have been at the alleged dinner with Ms McGonigle and Lord McConnell was named in court as Jim McCall.
The trial, which is taking place before Sheriff Douglas Allan, continues.