Discussions are taking place between Ofcom and the department for culture, media and sport (DCMS), according to Sky News, which first reported the news.
Former Treasury mandarin Lord Burns has been Channel 4 chairman since 2010. He is also currently a member of the Office for Budget Responsibility’s oversight board.
Previous roles include chairman of Santander, chairman of Marks & Spencer, and non-executive director at Legal & General.
The talks follow reports in recent months that the government is considering privatisation of the public broadcaster, known for programmes such as Hollyoaks and Gogglebox, a move which could net the Treasury around £1bn.
The government said in June that it had “no plans currently to remove the public-service conditions imposed on Channel 4 or to privatise it”, after sources claimed it was sounding people out.
And speculation was stirred up again in July, when former Channel 4 chairman Luke Johnson said a sale was “worth considering”.
Earlier this summer, DCMS also denied reports that it would sell off Channel 4’s London headquarters forcing the broadcaster to relocate to Birmingham in a bid to raise millions of pounds from the property on Horseferry Road in Westminster.
Channel 4 and Ofcom declined to comment last night.