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The actor and writer recently appeared on Allen's chatshow and was seen leaving a charity comedy gig with the popstar on Wednesday night.
A source told the Daily Star: "James and Lily hit it off when he appeared on her show and they’ve got closer.
"He's asked her if she wants to think about taking a part in his third series and she's chuffed to bananas about it. I think James has a bit of a crush on her."
Allen was allegedly thrown out of the men's toilets at the Teenage Cancer Trust show after she was caught giggling with Noel Fielding and Johnny Borrell.
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