The chief executive post is currently held by Robin Miller, who is also the Emap chairman. Miller stepped back into the chief executive's role last summer following the resignation of Kevin Hand, who left under a cloud following a disastrous foray into the US market which cost the company over £400m.
Emap is understood to have appointed headhunters to seek a replacement for Miller in May, although this has not been confirmed by the company.
Other potential replacements for Miller include internal candidates Gareth Hughes, who is finance director, and Tom Moloney, the company's chief operating officer. Paul Keenan, chief executive of Emap Consumer Media, is a popular choice among company insiders, following a rapid rise through the ranks in the last decade.
If Murphy left Carlton it would solve the problem of who would run a merged Carlton and Granada when media ownership rules are relaxed.
Murphy has already been touted as the future chief executive of a merged Carlton and Granada, working alongside Granada chairman Charles Allen.
Carlton and Granada are currently struggling to recruit a chief executive for the ITV network, after their preferred choice, Dawn Airey, signed a £1m-a-year deal to work for BSkyB's Sky Networks.
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