Davies said: "I'd like to be as good as Rio. I'm a big fan of his and I think he's the best, or one of the best, defenders in the world.
"He can do a bit of everything in the game. He doesn't mess about with the ball. When he needs to clear it, he'll do that.
"But, at the same time, he's got such good feet. He can come out with the ball, head it, do whatever he wants to do.
"If you look at Rio, he could play for another 10 years if he wanted to with the way he plays.
"For me to get anywhere near him ability-wise would be a big thing - and hopefully that would push me on to getting close to playing alongside him in an England shirt."
Davies admitted: "Whether it's alongside Rio or alongside anyone, I'd obviously love to play for England. That is my ambition.
"I've been on the substitutes' bench against Germany at the end of last year. It's time now that I start stepping up and trying to push myself back in there."