Pellistri, who turned 20 in December, spent the 2021/22 campaign on loan with Deportivo Alaves but has struggled for game-time recently, with the La Liga club being embroiled in a relegation battle.
The Basque club ultimately finished bottom of the Spanish top-flight, with Pellistri making 21 appearances.
Only five of those arrived after the turn of the year but Facundo has still enjoyed 2022 as he made his senior international bow in January, in a World Cup qualifier against Paraguay.
He also started in wins over Venezuela and Peru, as La Celeste recovered from an underwhelming start to easily book a place at the Qatar finals and Alonso believes the former Penarol player fits in well with his desired style of play.