According a report in the Financial Sunday Express, as a condition of allowing Allen and Green to split the top jobs of chief executive and chairman, shareholders want a heavy deputy chairman brought in.
The report claims that the call is being made on the back of the well-known differences between Granada's Allen and Carlton's Green. The two have differing management styles and have clashed in the past.
The report mentioned a number of senior figures who might take on such a role at a merged ITV company. The names include Jim Forbes, former chief executive of Scottish and Southern Energy; Derek Higgs, who was behind the recent government report on corporate governance; and Sir Roy Gardener, the chairman of Centrica.
The call follows recent rocky AGMs for Allen and Green.
Last week, Carlton shareholders aired their grievances about generous directors' pay packages. One in three Carlton investors opposed the remuneration packages of directors at the company and almost one in six failed to support Green's re-election as chairman.
Green's package was worth £707,000 last year and earlier this year he was awarded 1.4m share options.
It followed Granada's AGM in the previous week where one in four Granada shareholders voted against director's pay packages and chairman Charles Allen's two-year rolling contract.
Investor groups have been lobbying the two broadcasters over fears that directors may carry over their pay deals to the merged ITV.
Allen is under fire for his two-year contact, worth £2m in a golden handshake should he leave the company.
Institutional investors such as Schroders and Morley, which own almost 10% of Granada between them, are leading the fight.
Granada's merger with Carlton is currently being examined by the Competition Commission, which is expected to complete its inquiry by June 25.
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