Lygo, who joined Channel 4 as its director of television last November and previously worked as director of programmes at Five, when Airey was its chief executive, is reported to have decided to stay in his current post.
Lygo has told the media that he is not a candidate for chief executive as he has only recently taken on his role, which is where he said he could best serve C4.
Bazalgette, who applied then withdrew the last time the Channel 4 job was vacant, when Michael Jackson left for Universal in the US, has told the press that he is happy where he is and has no intention of applying for the job.
Airey has cemented her position as favourite with the odds of her taking the role now 5/4. Lygo's odds have now changed from 3/1 second favourite to 10/1. The odds for Bazalgette, who was 14/1, now stand at 33/1.
The new second favourite is BBC director of television Jana Bennett, whose odds remain at 5/1. Others names being mooted for the job are BBC director of factual and learning John Willis at 7/1; former Warner Music boss Roger Ames at 12/1; Talkback Thames chief executive Peter Fincham at 14/1 and former BBC governor Heather Rabbatts at 16/1.
The race to become Channel 4 chief executive follows the announcement last month that Mark Thompson is to switch channels, taking the vacant director general role at the BBC.
A Ladbrokes spokesman said: "What they (Bazalgette and Lygo) are saying does change the odds but it must be remembered that Mark Thompson also ruled himself out of his new job so they are not out of it yet."
Mark Thompson's leaving date is set to be announced next week.
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