Atletico see the Wales international as a potential replacement for Filipe Luis.
Davies, after recently penning a new deal, told Swansea's official website: "I think it's the right place to be at in terms of my career, and if I'm playing regularly and I'm happy then that's the main thing and all I can ask for.
"This is exactly what I would have wanted if I was to make it into the first team here, and fortunately I've been able to do just that.
"I'm very happy with how things have gone and it is great to get that reward for all the hard work over a period of time."
For breaking stories and all the great banter like us on Facebook: facebook.com/tribalfootball