Tuttosport says with the approval of coach Luciano Spalletti, Juve have contacted Palace this week about their France centre-forward.
Spalletti sees Mateta as a replacement for Dusan Vlahovic, who is coming off contract at the end of the season.
Juve would be happy to do business this month with Palace for their centre-forward, though will attempt to drive down their initial €30m asking price.
Spalletti has told his directors that Mateta fits his "profile" for the type of centre-forward he wants for his playing system at Juve.
This season, Mateta has 10 goals and two assists in 32 games.