The Frenchman will spend the rest of the season with the Spanish club, hoping that the move will allow him to play regularly for the first squad.
Pellistri is with the national team after receiving his first senior call-up for the important World Cup qualifiers against Paraguay and Venezuela.
Manchester United have agreed to loan Anthony Martial to Sevilla for the rest of the season.
Rashford scored the late goal for Reds to secure a thrilling 1-0 Premier League victory over West Ham United on Saturday.
Praising the team for keeping a clean sheet, De Gea was also happy that they did not concede many chances against one of the top-flight’s in-form teams.
Rangnick’s three substitutes - Anthony Martial, Edinson Cavani and Marcus Rashford - combined for the only goal of the match.
Rashford has now scored twice in two games for Manchester United, having scored the third goal after coming from the bench in Wednesday's 3-1 win against Brentford.
Marcus Rashford scored a last-gasp winner as Manchester United defeated West Ham United 1-0 in the Premier League fixture at Old Trafford on Saturday.
Manchester United host West Ham United on Saturday in a crucial match in terms of the Premier League top-four race.
Interim manager Ralf Rangnick believes the Portuguese star is best-suited to playing in a deeper no.8 role for United going forward.