While the singer spent a few seemingly romantic days getting dinner and going bar-hopping in NYC for John's 35th birthday, friends say she's acting hot and cold to keep him intrigued.
"She doesn't want to be just another one of his conquests," said the source, adding that the "Wide Awake" singer is sure she can "change him."
Katy's plan on getting John to settle down sounds a little unorthdox, though: She's agreed to an open relationship.
"She recently told John she was open to seeing other people," the insider continued. "Once Katy turned her back on him, he started chasing her again!"
This past summer it was reported that John put the brakes on the relationship when pals said she was falling "dangerously in love" with the singer.
John has dated everyone from Jennifer Aniston to Jessica Simpson to Taylor Swift, with all the women sharing a few grievances along the way.
Swifty immortalized their time together by penning a few not-so-subtle songs — "Dear John" and "I Knew You Were Trouble" — in which the country crooner tosses off lyrics like, "A new notch in your belt/Is all I'll ever be" and chastises the singer for taking advantage of a 19-year-old.