The 27-year-old singer, who recently filed for divorce from comedian Russell Brand, spent two nights flirting with the singer, reported Sun Online.
"They've been spending time writing together, or making sweet music if you want to put it another way, for her new album. They had a post session night out at Soho House in LA last weekend then met up for pizza at her gaff later in the week," a source said.
Guests at Soho House said "they were all over each other".
Mayer is the third guy Perry has been linked with since her split from Brand.
She had a brief fling with French model Baptiste Giabiconi