Cooke, who died last year aged 95, presented the longest-running series in history to be broadcast by a single person. He presented 58 years of weekly broadcasts from March 1946 with 'American Letter', which was renamed 'Letter from America' in 1949.
In July 2004, the BBC announced it was to produce a new programme called 'A Point of View' using journalists from across the US to reflect on everyday America in an attempt to attract younger listeners.
At the time, the BBC said the 10-minute programme was not a replacement for 'Letter from America', nor for Alistair Cooke, saying "some acts are simply impossible to follow".
The BBC is still in talks with New York-based Evans to host the show, made famous by Cooke for his wit and charm in making sense of the American century.
Evans edited the Sunday Times from 1967 to 1981 and The Times from 1981 to 1982. He is the author of a number of books on recent US history as well as 'Good Times, Bad Times' about his years at The Times newspapers.
Evans was born in Lancashire and is married to former Vanity Fair editor Tina Brown.
A BBC spokesman said: "We are hoping he will sign shortly and if he does it will be for a run of 13 weeks, as with Brian Walden, whose time will end shortly."
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