Atalanta signed Musso from Serie A rivals Udinese in the summer of 2021. The goalkeeper has since played 99 competitive matches and kept 32 clean sheets.
Musso helped win the Europa League last season and has two caps for Argentina.
Now Atlético Madrid have taken the 30-year-old on loan for the remainder of the season.
The Spanish giants have a mandatory purchase option if certain conditions are met.