The Sun claims that the couple - who have been dating for around four months - want to move in together in the few weeks and hope to be in a new rented pad by Christmas.
Despite their romance appearing to be going strong, K-Pez's friends are apparently convinced that the Teenage Dream star is 'making a terrible mistake' by getting serious with the notorious womaniser.
Even Perry's close showbiz pal Rihanna is thought to be 'wary' of John's reputation when it comes to his previous track record with women.
A source told the 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.”
They continued: "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 is even thought to have introduced Mayer to her highly religious parents, and is said to have taken the singer/songwriter to her local church.
The insider revealed: "Introducing John to her parents was a huge step for Katy and it proves she’s 100 per cent committed.
“She acknowledges she rushed into it a little quickly, but she is determined to trust her instincts and follow her heart."
They added: “Despite what the cynics may think, she is looking forward to moving in with John and says she’s happier than she’s been in a very long time.”
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