The 20-year-old, who has received plenty of plaudits for his form this season, has also reportedly sparked interest from Liverpool, Manchester United and Arsenal.
"The first I knew about Atletico was when a pal texted me the morning the story appeared," Davies told the Daily Mail.
"My phone beeped and there was this message saying, 'have you seen this? Atletico Madrid?!' I went online to see what it was all about.
"It is nice to hear something like that, because it clearly means you must be doing something right. It's got to be a boost for your confidence but it's not going to turn my head."
The Wales international has been at Swansea for his entire career so far.