West, 37, and McCartney, 72, have grown close in the recent months and the rapper is keen to collaborate with the Beatles star, reported Contactmusic.
Kanye and Paul have known each other for a long time but have become more friendly recently. There's every chance they'll head into the studio together," a source said.
West has apparently already started meeting up with the 'Can't buy Me Love' singer to work on new material.
"They've had a few meetings with each other but both of them always keep their collaborations under wraps until the last minute," the source added.
McCartney first expressed his interest in working with West in an interview last year.
He said though he had resisted the temptation to get a rapper in for his track 'Appreciate', West and Jay Z would be first in the running of potential collaborators.