They cant keep their hands off, this person said.
Ministers have shown in recent years that they are prepared to veto Channel 4 board members.
Channel 4 insiders have said it would be scandalous if the government does not approve non-white candidates.
Channel 4 chairman Sir Ian CheshireOfcom
Sources added that diversity has been big priority for Ofcom.
A spokesperson said: Ofcom is currently recruiting for vacancies on the Channel 4 board.
Channel 4s board is chaired by Sir Ian Cheshire, the former chief executive of retail group Kingfisher.
He was appointed in April last year.
