The 36-year-old singer has revealed the former Beatles rocker once asked her if the pair could ''jam'' together in the studio whilst she was working on her 2017 venture 'The Architect', but was disheartened when she failed to secure the iconic musician's talents on a track because he'd been left ''snowed under''.
Speaking to The Sun newspaper, Paloma said: ''He came to rehearsals and said, 'I'd love to jam with you'. He didn't make it but sent a cake with a note that said, 'Sorry, snowed under. Let's jam another time.'''
There's still hope for a collaboration between Paloma and McCartney, 75, in the future, although the 'Only Love Can Hurt Like This' hitmaker hasn't confirmed their rescheduled ''jam'' date.
It comes after Paloma recently claimed she has become a ''better'' singer since welcoming her first child with her partner Leyman Lahcine in December 2016, as it has made her ''lung capacity bigger''.
She said: ''I never really felt I was a proper singer. I always felt like I was a sort of impersonator of a singer for a long time. You can even listen to my first album and hear it, that I wasn't very good then. I've learned later in life and on the job.
''And this is going to sound mad, but I feel like I can sing better now I've had a baby, that something's changed in my body. My lung capacity is bigger and I feel more alive and stronger, more enduring, and that's affected my voice and opened something up in my brain that's saying 'you can'. Before there was a 'you can't', an almost physical inability.''
Securing a collaboration with McCartney may put Paloma's mind at ease, as the 'Never Tear Us Apart' singer is always worried about whether or not her next album will mark the ''ruination'' of her career.
She said previously: ''I always feel like the next one's the one that's going to be the ruination of my career. I start thinking, 'OK, what am I going to do if this doesn't work?'.
''I don't think it is irrational in this current music climate because look at some of the massive artists that came out at the same time as me - like Duffy, where's Duffy? I don't think anything's guaranteed, everything's changing. With this album, Spotify is the most powerful thing on the planet now, and I don't have a Spotify following, so I am literally trying to build it now.''
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