The 'Wide Awake' singer - whose divorce from Russell Brand was finalised earlier this month - was seen enjoying a romantic meal with the 'Gravity' singer at the Chateau Marmont in Hollywood Wednesday night and onlookers say they looked totally smitten with each other.
One source told Us Weekly magazine: "They were holding hands across the table, sneaking kisses, and laughing."
They were then pictured leaving the exclusive venue in John's car.
However, sources the pair - who have been seen out together on a few occasions over recent weeks - aren't serious about each and are just having fun.
A source added: "They're just hooking up right now. It's not serious - yet!"
Katy - who had been seeing Florence + the Machine guitarist Robert Ackroyd - recently said she was waiting for a man to woo her.
The 27-year-old pop beauty said: "I'm a woman who likes to be courted, strongly. Never say never, I guess you'd say. I'll let love take the lead on that."
John has previously dated Jennifer Aniston, Cameron Diaz and Jessica Simpson.