The former doctor, known for his bald head, big collar and black specs, is thought to earn around £1m a year from his ITV contract, which is believed to run out next year.
It is understood that if he signs a deal with the BBC he will still be able to continue hosting 'Harry Hill's TV Burp' on ITV, which has had seven series so far and has grown into a Saturday night ratings stalwart.
Hill was recently BBC director general Mark Thompson's guest of honour in a private box at The Proms.
A BBC source said: "Harry is one of the top comedians on TV. Crucially he is someone who appeals to the whole family, so he would be perfect for the BBC on Saturday prime-time presenting a show like the Generation Game.
"If the BBC make a formal approach expect a real tug-of-war. Let's be honest, he's the only funny thing on ITV."
Hill joined ITV in 2001, when he started presenting 'TV Burp', and has also been the host of 'You've Been Framed' since 2004.
His 'TV Burp' show won two Baftas this year for Best Entertainment Programme and Best Entertainment Personality.
The comedian has also had a number of voice-over roles on TV ads, thanks to his recognisable voice, as well as appearing in 'Comic Relief' ads. He once sung a song called 'Bring on the Branston!' for the Branston Pickle ads but his appearance in a Boots' 2004 Christmas ad earned him a 北京赛车pk10 .
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