The Uruguay international will ply his trade in La Liga after securing a switch to Nuevo Estadio de Los Carmenes.
The 22-year-old, who signed for the Reds in October 2020, has played in Spain before, enjoying successful consecutive loan spells with Alaves.
This season, Pellistri has represented United 14 times and will now join Nazaríes to further his experience.
He was an unused substitute at the weekend, as Erik ten Hag's men progressed past Newport County in the Emirates FA Cup. His last outing for the Reds came in the previous round, in the 2-0 victory at Wigan Athletic.