The 35-year-old star is currently preparing for the arrival of her first child with Orlando Bloom, and the pregnant singer has already asked Jennifer, 51, to fulfil the role in her daughter's life.
A source told the Sunday Mirror newspaper: ''Katy and Jen are very close. During lockdown, they went for socially distanced walks, and spent lots of time catching up.
''She is pretty chuffed about it as well and cried when they asked her.''
Jennifer is already the godmother of 'Friends' co-star Courteney Cox's 16-year-old daughter Coco.
Katy recently revealed she calls her unborn child 'Kicky Perry'.
Speaking about her pregnancy experience, the 'Dark Horse' hitmaker - who is engaged to Orlando - shared: ''I am waddling like a duck!
''I'm breathing heavily, I'm a full-on mouth-breather. And um yeah, it's loud and obnoxious and, oh my God, I just eat so much flavoured ice! It's like put all the ice in my mouth, right now!
''I call her Kicky Perry sometimes. I love a pun but I'm really active right now and, you know, my doctors are like, 'Stay active, you're good to go, girl!' And so I've been dancing, I've been singing a lot.''
Katy also admitted she's grateful that Orlando - who has Flynn, nine, with ex-wife Miranda Kerr - already has parenting experience.
She said: ''The good thing is that he has a kid that's nine. And he's been through it.
''So when we were going to pick out strollers, he knew exactly the stroller. And like, some of the strollers are very chic, they've got leather handles and blah, blah, blah. And I was like really drawn to them right? And he's like, 'No, let me show you what the stroller is. It's this one that you pick up in the middle and it collapses and it's like, 'Bang, bang', it's like an umbrella'.
''I was like, 'Oh my God, I'm so grateful that you know this, 'cause I would have gotten some, you know, large hunky thing' and that is avoidable because he's already had a test run so, I'm grateful for that.''
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