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The 2000 Olympic super-heavyweight champion is backing fellow Briton Joshua to be too strong for American Charles Martin in Saturday's IBF world heavyweight title fight in London.
Harrison says "all the cards are in Joshua's favour", likening the 26-year-old to the ex-heavyweight champions.
"He lives the life of an athlete," Harrison, 44, told BBC Radio 5 live.
"He's very fit, strong and committed.
"I just think Anthony Joshua has got that George Foreman, Frank Bruno brutish strength - that ingredient that is hard to hold him off."
Watch: Anthony Joshua, Beast Mode
Martin has won 23 and drawn one of his 24 fights and beat Vyacheslav Glazkov for the vacant IBF belt in January.
Harrison has sparred with the 29-year-old American, whom he calls a "rugged, tall, big southpaw", but says Watford-born Joshua will have the British crowd behind him on Saturday.
"Charles Martin will be gallant, brave and it's a great fight potentially" said Harrison. "But I can't see him keeping back the steam train that is Anthony Joshua."
Anthony Joshua has the "brutish strength" of George Foreman and Frank Bruno, according to Audley Harrison.