The couple were photographed in a car together last night (August 1) after dining at Los Angeles's popular restaurant Chateau Marmont, Us Weekly reports.
One onlooker claimed that the couple were "holding hands across the table" during their meal, as well as "sneaking kisses" and laughing.
However, another source alleged: "They're just hooking up right now. It's not serious - yet!"
Perry and Mayer were first spotted together in June, with reports at the end of last month saying that they had been "all over each other" during a visit to Soho House.
Since her divorce from Russell Brand, Perry has been romantically linked to people such as model Baptiste Giabiconi and Florence + the Machine guitarist Robert Ackroyd.
She recently confessed that she is "a woman who likes to be courted".