John Mayer and Katy Perry: On the Road to Romance?

08/02/2012 at 11:05 AM EDT

Katy Perry, John Mayer Dating? The Pair Have a Dinner Date in Los Angeles
Katy Perry and John Mayer

John Mayer

John Mayer

Katy Perry

Katy Perry

Budding romance?

John Mayer and Katy Perry were spotted leaving the Chateau Marmont Wednesday in Los Angeles, where the singers reportedly had a dinner date.

And indeed, a friend of Perry's tells PEOPLE that the pair have been chatting on the phone and have gone out a few times – but they're taking things slow.

"I don't think either of them are trying for anything serious right now. She's not talking like he's 'The One,' " the pal says. "She's comfortable around guys who understand the craziness of that world, which he definitely does."

Mayer, 34, has been involved with a long line of high-profile women, including Jennifer Aniston, Taylor Swift and Jessica Simpson.

Perry was recently divorced from Russell Brand, and dated Florence + the Machine guitarist Robert Ackroyd earlier this year.

She tells Elle in its new issue that she hasn't given up on love, calling herself "a woman who likes to be courted – strongly."

On the topic of potentially getting married again, she adds, "Never say never ... I'll let love take the lead on that."

Reporting by STEVE HELLING

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