She admitted in an interview with ABC News Radio: ''I said to her, 'Katy, let me tell you something. You don't have any rivals. So forget that. Never say that word again...
''You don't have rivals. All of those girls? Friends. You'll probably work with all of them at some point. Friends.' ''
The pair ended up chatting until the early hours of the morning and formed an unlikely friendship when they met in London to perform their respective concerts Fleetwood Mac at the O2, and Katy at the iTunes Festival.
Stevie, 65, added: ''I met her after her rehearsal at 11:30 [pm]. I thought it was going to be a 20-minute, 'Hey, how are you doing?' thing - and we sat for three hours until, like, three in the morning. And we pretty much talked about everything.''
Katy quizzed Stevie about her own musical rivals and the rocker was flabbergasted because the situation in her own 80s heyday was completely different.
He also slapped a jet-lagged Taylor Hawkins.
The acclaimed performer had just cancelled touring due to a battle with cancer.