The British royal is said to have become smitten with The Saturdays vocalist after they were introduced by mutual friends at a polo match in 2010, but they only started dating recently after she split from model David Gandy after two years together.
A source told the Daily Mail newspaper: ''They have been to Public nightclub a couple of times and get along well. It's ironic because Mollie fell for David over Prince Harry, but now she seems very taken with Harry.''
In recent weeks Mollie, 24, and Harry, 27, have been at the same London nightspots including Public and karaoke bar Bunga Bunga, but always left separately, as they are keen to avoid any publicity.
The source added: ''They're having a lovely time together but she won't say anything publicly because she knows that will mean the end of it.
''She loves the publicity so she is happy to drop a few hints and keep people guessing.''
Palace aides have not commented on the relationship, but Mollie did proclaim her affections for Harry, a baby African hippo, who is named after the prince, and has become an internet sensation after he was rejected by his mother and is being raised at a sanctuary in South Africa.