Williams, who co-hosts the show with Bill Turnbull, confirmed earlier this month that she is quitting the programme ahead of its move north to Manchester.
The BBC revealed that the host and sports presenter Chris Hollins are among 54% of the morning show's team who have declined to relocate to Salford next year.
However, according to The Mirror, Cohen remains confident that the programme will retain its viewing figures and lead over ITV1 rival Daybreak.
"I'm not massively scared," he said. "The show and format is always more important."
Director of BBC News Helen Broaden previously insisted that the show will continue to go "from strength to strength" in its new home.
> Andy Townsend 'to join BBC Breakfast'