The ITV football presenter was asked by the BBC if he would like to take a seat as one-off presenter of the show, which was due to be broadcast later this year, following in the footsteps of presenters including Five news anchor Kirsty Young, who did a star turn on the show recently.
However, ITV chiefs nixed any chance of the housewives' favourite appearing on the humorous current affairs quiz alongside regular captains comedian Paul Merton and Private Eye editor Ian Hislop.
Lynam told the Daily Mirror: "I was very keen to do it but was told I couldn't. If the BBC ask again, once my contract is over, I'd love to do it. But the offer might not be there by then -- because they may have found a permanent presenter."
'Have I Got News for You' has had a series of guest presenters after the BBC sacked Angus Deayton. He lost his 'Have I Got News for You' presenting job when a prostitute told the News of the World how she romped with Deayton while he snorted cocaine.
The BBC decided that his position had been "unacceptably compromised" and sacked him from the programme in October 2002.
For Lynam, the 'Have I Got News for You' knockback follows speculation that he might return to the BBC to host a new show of his own once his contract at ITV expires next year.
Lynam has said that he plans to switch from sports broadcasting after the Euro 2004 football championships in Portugal in July and look for new TV projects.
If Lynam says yes to a BBC deal it will mark a return after four years. Lynam left the BBC to join ITV when it won the TV rights to Premiership highlights. Prior to his departure from the BBC, Lynam had spent 30 years at the corporation.
Lynam's agent Jane Morgan said: "He feels it is a good time to go and he has three projects on the drawing board, one of which is sports-related, but not sport per se. If the BBC were interested in looking at this we would be delighted."
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