Shaw has not had to come up against his teammate often in practice sessions this season due to Pogba's persistent injury problems.
Asked who he fears being up against in training, Shaw replied: "I wouldn't say 'fear' is the right word because I enjoy playing against the likes of Rashy and Martial because they're tricky, high-quality players and I like that challenge of facing them."
He told the club website : "Every time I'm facing Anthony, I like to have a little joke around with him, talk to him a lot and tell him: 'I'm coming for you.'
"Actually, probably the hardest player to get the ball off is Paul. He's so big, strong, he's got quick feet. To be fair, he's got everything to be the best midfielder in the world.
"You could ask any player in the team about that. I'd have to pick Paul as the toughest one to train against as well because it's so tough to get the ball off him – he knows how to shield it away and he's also got the best quality to deliver shots and passes too."