Eyre was chief executive at ITV in the late 1990s and more recently chairman of GCap Media until the company was sold to Global Radio in 2008.
he and Lord Alli, who is famous for co-founding the production company behind The Big Breakfast but currently the chairman of Chorion and ASOS.com, have been shortlisted for the chairman role.
The Channel 4 appointment is made by Ofcom, which is said to be keen to have a woman take the top role. While the broadcaster is famous for recruiting its chairmen from outside the TV industry -- current chair Luke Johnson made his fortune running the Pizza Express restaurant chain -- a number of heavyweight female candidates are thought to have turned down the opportunity, including Dame Majorie Scardino, who is chief executive of Pearson, and Dianne Thompson, who holds the same role at Camelot.
Eyre's background is in ad agencies, before he moved into commercial radio in 1991, when he took up the role of chief executive of Capital Radio. He joined ITV as chief executive in 1997, remaining there until 2000 when he became the chairman and CEO of Pearson Television.
Eyre also holds a number of non-executive roles at bodies including the Guardian Media Group and 19 Management, and he is chairman of the IAB.
The Telegraph also reports that ITV has been turned down by another potential candidate for the chief executive role after Pascal Cagni, who heads Apple's operations in Europe, ruled himself out of the running. Other candidates to rule themselves out are Tony Ball, former chief executive of BSkyB, and HMV chief executive Simon Fox.