The moody guitarist usually stays in hotels when he is visiting from New York, despite owning a place in California.
So Katy decided to give her spare set to the rocker, and has told him to stay at her house when he is in town, reports The Sun.
A source told the tabloid: "John thinks it is easier to stay in hotels rather than his own L.A. pad.
But Katy insists he should stay with her. She thinks it makes sense."
The I Kissed A Girl singer first fuelled romance rumours in August when she and John enjoyed dates at the Chateau Marmont Hotel, but their fling was said to have been called off just a few weeks later.
They were then seen all over each other again at L.A.'s FYF Fest earlier this month.
Katy, who was married to Russell Brand, faces a tough task taming John - his List of exes includes Jennifer Aniston, Taylor Swift, Jessica Simpson, Jennifer Love Hewitt, Minka Kelly and even Miley Cyrus.
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