Perry and Ackroyd have apparently been dating for about a month, after they were seen together at the Coachella Music Festival in April.
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One source told Us Weekly: "It wasn't that serious. It's not a nasty thing and they are still talking, but Katy told him to do his thing and they'll talk soon."
"No hard feelings," another source claimed. "She's really busy and so is he."
Perry, who was previously married to Russell Brand, recently performed her new single 'Wide Awake' at the 2012 Billboard Music Awards on Sunday night (May 20).
Perry can also be seen in her new concert film Part of Me 3D, out on July 5.
Watch the trailer for Part of Me 3D below:
