The Sun reports that the actor and presenter is being lined-up to front a revival of the comic game show, with a test episode set to be filmed soon.
Paddy McGuinness has also been mooted to front the revived format.
The format was revived in 1997 with Paul O'Grady (as Lily Savage). It switched to ITV in 2001, finishing in 2002. However, in 2016 ITV commissioned a one-off Christmas special with David Walliams hosting. The show now looks set to return to BBC One.
"Bradley is the favourite to be the new host but bosses behind the reboot also have discussed Paddy McGuinness and Rylan Clark as potential hosts. A pilot is being filmed later this year and if it's a success, it'll go on to become a new series. Everyone is confident it'll be a hit and it's a perfect fit for Saturday night. It's likely to nab a primetime spot and cash will be pumped into the series if it does go ahead.
"Plans are still being worked on and the presenter has yet to be set in stone, as well as who'll make up the first celebrity panel but it's all very exciting. There is a hunger for fun, family programming and nostalgia seems to be a winner every time."
The BBC has yet to officially comment on the plans.
Aside from hosting The Chase, Bradley Walsh has in recent years fronted ITV variety show Tonight At The London Palladium, and acted as a team captain on sports-based panel show Play To The Whistle. As an actor, he'll next be seen on screens playing Pop Larkin in the new version of The Darling Buds Of May.
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