The One Direction singer is said to have become determined to meet the Oscar winner, and started following a fake Twitter account.
A source said to Heat: "Harry first noticed her during the Golden Globes and one day he YouTubed loads of videos of her and loved how funny and self-deprecating she was.
"He even wrote about his crush on his Facebook page, describing Jennifer as 'perfect'. He was hoping to start chatting to her casually on Twitter - he's done it with loads of celebs before - but didn't realise it wasn't the real Jennifer Lawrence."
The insider added: "He's not getting ahead of himself, but he'd love to meet her - though she's one of the few girls he might not be able to keep his cool around."
Previously, Styles was linked to Taylor Swift, whose new video '22' is rumoured to be about their split.
Photo gallery - Harry Styles's rumoured girlfriends:
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