The Beatles legend has revealed he wanted to duet with the pop superstar as they were both set to headline the 50th anniversary of the iconic festival, which was sadly cancelled due to the coronavirus pandemic.
Speaking together for Rolling Stone magazine, Taylor said: "Wow, it would’ve been so fun to play Glastonbury for the 50th anniversary together."
McCartney agreed, adding: "It would’ve been great, wouldn’t it?
"And I was going to be asking you to play with me... I would've done 'Shake It Off.' "
With the live music industry effectively put on hold during the pandemic, both musicians released new albums, with Taylor's 'folklore' dropping in July, while 'McCartney III' is set to drop on December 11.
She pondered: "I was wondering about the numerology element to McCartney III. McCartney I, II, and III have all come out on years with zeroes."
Macca explained: "Ends of decades... This was being done in 2020, and I didn’t really think about it. I think everyone expected great things of 2020.
"'It’s gonna be great! Look at that number! 2020! Auspicious!' Then suddenly Covid hit, and it was like, 'That’s gonna be auspicious all right, but maybe for the wrong reasons.'
"Someone said to me, 'Well, you put out 'McCartney' right after the Beatles broke up, and that was 1970, and then you did 'McCartney II' in 1980.'
"And I said, 'Oh, I’m going to release this in 2020 just for whatever you call it, the numerology...' "
Taylor admitted that numbers are important for her, with 1989 - the year of her birth - and 13 both holding special significance for her.
She said: "Yeah, it’s lucky for me. It’s my birthday. It’s all these weird coincidences of good things that have happened.
"Now, when I see it places, I look at it as a sign that things are going the way they’re supposed to. They may not be good now, they could be painful now, but things are on a track. I don’t know, I love the numerology."