The race follows the announcement last week that Mark Thompson is to defect to the BBC as its new director-general.
Ladbrokes is tipping Airey as the 6/4 favourite, followed by Channel 4 director of television Lygo at 3/1.
Other high-rating contenders include the BBC's director of television Jana Bennett at 5/1 and the BBC's director of factual and learning John Willis at 8/1. The two were also linked to the race for the director general's job.
Also in the running are former Warner Music boss Roger Ames, who is tipped at 14/1; Endemol head Peter Bazalgette at 14/1; former BBC governor Heather Rabbatts at 16/1; BBC Sport head Peter Salmon at 20/1; and BBC head of radio Jenny Abramsky at 33/1.
At the weekend, Channel 4 chairman Luke Johnson claimed that there was only a short list of people in the media industry who could fit the bill. He said the right candidate needed a combination of experience in the media sector and a business track record.
Airey certainly fits in with this. She joined Sky from Five where she was chief executive and has also worked at Channel 4 as head of arts and entertainment. She shocked the industry in 2002 when she took up the Sky role because she was expected to take a role at ITV as director of channels to replace David Liddiment.
Airey's former colleague Lygo also worked at Five as director of programmes before making a return to Channel 4 earlier this year.
According to reports, Lygo is likely to have a say in the appointment. It is understood that the last thing that Johnson wants to do is upset the television director, because he is regarded as an asset to the channel, being responsible for top-rating shows such as 'So Graham Norton', 'Trigger Happy TV', 'Smack the Pony', 'Spaced', 'Black Books' and 'The Ali G Show' during his first term at Channel 4.
The appointment of Thompson, who is on a six-month notice period, as the BBC's director-general was made on Friday and the BBC is currently trying to negotiate a deal to get him on board as soon as possible.
Thompson's defection is said to have considerably irritated Johnson, who is now negotiating with BBC chairman Michael Grade over Thompson's contract.
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