Lambert was editor of the Financial Times between 1991 and 2001 and launched the US edition in 1997. He was replaced by Andrew Gowers, who did not last long in the role, leaving last year after clashing with FT executives over the newspaper's web strategy.
Lambert sits on the Bank of England's Monetary Policy Committee, which sets interest rates, but his term ends in May. The BBC is reporting that Lambert will take over from Jones in July.
As well as sitting on the MPC, Lambert has written government reports on BBC News 24 and the relationship between higher education and business. His report on the BBC news service led to its relaunch.
He started his career as a trainee at the Financial Times in 1966. Before his retirement from the FT, he edited the Lex column between 1974 and 1979, was New York bureau chief from 1982-1983 and deputy editor from 1983 until 1991.
The CBI lobbies the government on behalf of British business. Sir Digby Jones has been director-general of the CBI since 2000.
He originally signed a five-year non-renewable contract to head the consortium but at the request of members his contract was extended for a further two years, and was due to end on December 31 2006.
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