Lynton is understood to have been named on a shortlist, which also includes Mark Thompson, the director of television at the BBC.
His name emerged following the second round of interviews last week, ahead of a scheduled Monday board meeting.
As many as 10 candidates are understood to have applied for the job, left open when Michael Jackson unexpectedly quit to join USA Entertainment, part of USA Networks, in July.
Channel 4 has remained tight-lipped about the names of potential successors to Jackson. However, there has been a great deal of speculation in the industry about who has applied for the job.
The most recent shortlist reported in the media emerged after TV producer Peter Bazalgette and Channel 5 chief executive Dawn Airey withdrew their names from the race. Lord Waheed Alli, founder of Big Breakfast production company Planet 24, is also thought to have withdrawn last week.
Others who are believed to be on the shortlist with Lynton and Thompson include Peter Finch, the head of Talkback Productions, the company behind They Think It's All Over and Jana Bennett, the former head of science at the BBC.
The selection panel has been headed by Channel 4 chairman Vanni Treves with the help of director of programmes Tim Gardam, once the favourite internal candidate for the post, and managing director David Scott.
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