The 'Yeezus' rapper - who is reported to have become good friends with Paul, 72, in recent months - has approached the former Beatle about working together as he puts the finishing touches to his upcoming seventh studio album.
A source told The Sun newspaper: "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.
"Kanye really respects music legends and is still putting the finishing touches to his new album.
"He has been tapping Macca up for a while about working together.
Kanye, 37 - who is married to reality TV star Kim Kardashian West - has already started meeting up with the 'Can't buy Me Love' singer to work on new material.
However, the superstar pair are keen to keep the details of their team-up a secret.
The source added: "They've had a few meetings with each other but both of them always keep their collaborations under wraps until the last minute."
Paul first expressed an interest in collaborating with the 'Stronger' hitmaker - as well as fellow rapper Jay Z - last year.
Discussing his track 'Appreciate', Paul revealed he had '"resisted the temptation to get a rapper in," but added Kanye and Jay Z would be first in the running of potential collaborators.
When asked who would have been given the honour of appearing on the track, he replied: "Oh, Jay Z, Kanye."