The 30-year-old rejoined Estudiantes on loan during the January transfer window after struggling to secure regular action at Old Trafford in the first half of the 2019-20 campaign.
Rojo only made one appearance for the Argentine outfit before the coronavirus outbreak halted play, though, and his loan deal with El Leon has now expired.
The versatile defender is allegedly heading back to Old Trafford, where he has a contract until next summer.
However, according to El Dia, there is a chance that Estudiantes could sign Rojo on another six-month loan, with United set to hold talks with the South American at the end of July.
The former Sporting Lisbon left-back has made 122 appearances for the Red Devils in all competitions.