The One Direction hunk is said to have enjoyed a string of secret meetings with the brunette model - who he was first romantically linked with last December - including in London's private members club Shoreditch House and Greek restaurant Lemonia in Primrose Hill, and the pair went to great lengths to ensure they weren't pictured together.
A source said: "When they see each other they keep it very private, suggesting it's more than just a friendly hang-out."
Harry - who has previously dated stars including Taylor Swift and Kendall Jenner - is keen to "get to know" Daisy, 25, better and they are taking their romance slowly.
The source added to the Daily Star newspaper: "Harry's always liked Daisy's style and now wants to get to know her properly over time.
"He was even spotted visiting the Primrose Hill pet shop last week with her dog in tow."
Daisy previously dated former 'Doctor Who' actor Matt Smith, but they split last year after three years together.
Harry, 20, and Daisy were said to have first got together at mutual friend Alexa Chung's birthday party and shared an instant connection.
A source previously said: 'When Harry met Daisy there was a real spark. When they see each other they make sure it's in private at night or with a group of friends.''