The Firework singer and the renowned womaniser - who have been dating for four whole months - want to take the next step in their relationship and have been house-hunting in Los Angeles.

Apparently they're hell bent on finding a place before Christmas - on account of the world spinning faster in Celebrity Land. 

A source told The Sun: "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." Which is invariably the same mentality that got her together with renowned womaniser Russell Brand.

Sources say the couple - who had a brief split in October before getting back together - are totally smitten and like to spend every moment they can together. Like most people in the throes of a fledgling relationship. Those darn pheromones.

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 Brand ended a year ago this December - has already introduced John to her parents as she knows the romance is serious. I'm sure they're thrilled.

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, Taylor Swift, Jennifer Aniston, Minka Kelly, Rashida Jones, Renee Zellweger, and Cameron Diaz. He's also worn the face off Perez Hilton. He was 100 per cent committed to all of them.