While Perry has been linked to producer Diplo, she and Styles recently met up to enjoy dinner, reported Femalefirst.
"They like each other Katy and DJ Diplo are casually dating, but she's developed a huge crush on Harry, which she calls unexpected," a source said.
"He looks up to Katy and loves that she isn't your typical needy twenty-something."
Styles, 20, reached out to offer the 29-year-old beauty advice following her apparent falling out with his ex-girlfriend Taylor Swift, after the country star gave an interview and spoke about a "straight-up enemy" widely assumed to be Perry.