The Fab Four star joined the Gavin & Stacey creator in a fundraising sketch for British charity Comic Relief in 2011, in which he was shown telling Corden he was too "tubby" to go to Africa on an aid mission.
Now the comedian has revealed how he used strong-arm techniques and light-hearted bribery to convince MCCartney to take part in the spoof.
Corden tells U.K. chat show host Graham Norton, "I laid it on very thick, telling him, 'People won't die if you do our sketch'. It makes it very difficult for people to say no. He said, 'B**ody hell James, I've heard some groveling in my time'. I then said, 'That's nothing, if you'd said no I was going to say I would name my unborn child after you,' to which he said, 'If you promise to do that I'll do the sketch'. And that's why my son is called Max MCCartney Kimberley Corden."