The One Direction star asked Harris out while they were both at the W Westwood earlier this month, Life & Style says.
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"He asked for her number and said, 'Are you busy tomorrow night?'" a source claimed. "'I'd like to take you out to dinner if you're free'."
However, Harris has revealed that she is not interested in a romantic relationship with the 18-year-old singer, saying: "Harry is cute, but I could never date a guy that young. Never."
Harris is the latest star to be linked to Styles, who is also rumoured to be dating Lily Halpern and Irish photographer Sarah-Louise Colivet.
Rihanna recently described Styles, who split from television presenter Caroline Flack earlier this year, as a "star".
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