TV
BBC
Britton, 51, announced that she would be stepping down from the high-profile show last month after 10 years.
Bleakley, 29, currently co-presents the BBC's One Show and is said to be eager to join Phillip Schofield on the couch.
An industry source told The Sun: "Christine's people have told bosses that she would be interested - she is really keen. She would actually be good as the One Show viewers like her."
A number of candidates have been linked to the role since Britton's revelation, including Emma Forbes and Melanie Sykes. The source said competition was stiff, adding: "Everyone wants this job - it's THE job to get."
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