The 30-year-old re-joined Estudiantes on loan during the January transfer window after struggling to secure regular action at Old Trafford in the first half of the season.
Rojo only made one appearance for the Argentine outfit before the coronavirus outbreak halted play, though, and his loan deal has now expired.
However, according to TyC, United have thus far not accepted any offers for the versatile defender, who is now set to return to England to link up with his parent club.
The report claims that Estudiantes have not given up hope of signing Rojo, with the South American allegedly due to hold talks with United over his future upon his return.
The Red Devils are thought to value the former Sporting Lisbon left-back in the region of £15m.