The pair were spotted kissing backstage at his Newcastle gig earlier this week, according to The Sun.
The Roc Nation singer has been supporting Drake on the UK leg of his tour.
"Rita and Drake have been good friends for a while now but things seemed more serious this week," a source said.
"They were all over each other backstage at the gig on Monday (April 23) and weren't trying to hide it."
Drake wrote Ora's new single 'R.I.P.' and originally pitched the song to Rihanna.
The 'Hot Right Now' singer was previously linked to Rob Kardashian.
Watch Rita Ora in her video for 'R.I.P.' featuring Tinie Tempah below: