The former Financial Times editor may have an influential backer - Gordon Brown is said to be rooting for him to become BBC chairman.
After leaving the FT in 2001, Lambert, 59, was commissioned by the government to write a report on the BBC's 24-hour news channel.
The report criticised News 24 for not being distinctive enough, a point the BBC tried to address when it revamped the channel last year.
Despite his knowledge of the corporation gleaned from compiling his report, Lambert has no direct experience in broadcasting, having spent 35 years entirely at the FT, rising to become editor in 1991.
He now serves as an external member of the Bank of England monetary policy committee, giving him a say in interest rate decisions, and recently wrote a report on links between universities and business.
It emerged last year he turned down a knighthood in 2002.
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