Katy Perry and John Mayer
08/02/2012 at 09:00 AM EDT
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