The pair are currently on duty with the under 21 Italian national team at the European Championships, and enjoyed encouraging seasons with the Orobici.
According to Tuttosport, the Yellow Submarine has been monitoring the two players this season, and want to bring them to the La Liga in the coming months.
Villarreal will face competition from Juventus however for Zappacosta, while AC Milan and Inter have been long-term admirers of Baselli and are prepared to fight for his signature.
The Spanish club have been active in the transfer market since the season concluded, bringing in Paris Saint-Germain goalkeeper Alphonse Areola on loan and Malaga pair Samuel Garcia and Samuel Castillejo.
Baselli netted twice in 22 appearances, while Zappacosta appeared in 29 matches, netting three goals.