Katy Perry and John Mayer

Are Katy Perry and John Mayer cohabiting?

The couple that many gave no chance are now planning to move in together, a report says.

The 'Firework' singer and the renowned womanizer - who have been dating for four months - want to take the next step in their relationship and have been house-hunting in Los Angeles and aim to find a place before Christmas.

A source told The Sun newspaper: ''John and Katy have decided to give it a proper go and want to find a place in LA to share.

''But lots of people are willing them to fail. They row a bit and have quite a turbulent up-and-down relationship, despite it only being a few months old.

''Many of her friends are certain it will all end in tears.

''But that's brought them closer in a way. It's given them an 'us against the world' mentality.''

Sources say the couple - who had a brief split in October before getting back together - are smitten with each other and like to spend every moment they can together.

One said: ''They are together virtually every day.

''They hang out at John's place, cooking, watching movies and playing music.

''They take the odd trip away but generally they're trying to keep it behind closed doors.''

Katy - whose 14-month marriage to Russell Brand ended last December - has already introduced John to her parents as she knows the romance is serious.

The source added: ''Introducing John to her parents was a huge step for Katy and it proves she's 100 per cent committed.''

John has previously dated Jessica Simpson, Jennifer Aniston and Cameron Diaz.

© Bang Showbiz