The `One That Got Away` hitmaker has decided not to pursue a relationship with the Florence + the Machine guitarist - who she met at last month`s Coachella Music Festival - because she felt their respective working commitments would make seeing one another regularly too hard.
A source close to Katy - who separated from husband Russell Brand in December after 14 months of marriage - said: "The main thing which led to her split with Russell was spending the majority of her marriage to him on tour and she said dating Rob felt like being with -Russell all over again.
"It`s a shame as they both liked each other but Katy wants to be able to have a relationship with someone she isn`t constantly having to work out what time zone they`re in.
"Rob was gutted but Katy said she didn`t want to get in too deep and then break his heart so it was best to cut things off before they got serious."
The split has come as a shock to friends as Katy had appeared smitten with the musician and they were in "constant" contact.
The source added to the Sunday Mirror newspaper: "Rob was the first guy Katy had been with since splittingfrom Russell.
"She was still extremely fragile but had told pals their two weekends at Coachella together made her feel `sexy and alive` again.
"Even when Rob left to continue touring -America with Florence they would speak on the phone up to three times a day and she`d be constantly texting him."