The Uruguayan joined United in October of last year, but went out on loan to Alaves in the winter transfer window.
19-year-old Pellistri impressed for the La Liga side, helping them to avoid relegation this past season.
According to Noticias de Alava, Alaves want to extend Pellistri's loan spell for the entire upcoming season.
United are not sure if they want to loan him out again or give him a chance in Ole Gunnar Solskjaer's first team squad.
The two parties will speak and hash things out in the coming days.