Davies is rated as one of the top young full backs in world football, given his impressive displays for Bayern and the Canadian national team.
Davies, however, told his followers on the social media platform TikTok that he has great admiration for United and England star Shaw.
The latter had an outstanding Euro 2020 as England reached the final on home turf.
"I just saw one [comment] like: 'Luke Shaw is clear'," said Davies. "Can someone explain it to me? I want to know what that means."
A fan responded, saying "clear" meant Shaw was better than Davies at present.
Davies added: "Oh okay, I get it now, it means he's better.
"Yeah, I mean, he is! He's a really good player."
Need a VPN? Or seeking to switch? Then support Tribal Football by clicking here to sign up with our official partners NordVPN. Not only will you receive the best VPN experience, but also great discounts by signing up via Tribal Football. Thanks for your support!