Rojo began his professional career with Estudiantes, having progressed through the La Plata club's youth ranks.
Rojo is far from such an established fixture at United, having shuffled between left-back and centre-half while suffering injury setbacks during his two seasons under Louis van Gaal, but outlined similar career plans in an interview with TyCSports.
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"I miss the club, my family and my friends," said Rojo, who has also represented Spartak Moscow and Sporting CP during his time in Europe.
"I want to return to Estudiantes once I finish my contract in England."
Argentina - chasing a third consecutive victory - return to action in the Conmebol 2018 World Cup qualifying section on Tuesday, hosting Bolivia in Cordoba.
Rojo does not want his team-mates to take Bolivia lightly as they aim to close the five-point gap to group leaders Ecuador, who left Buenos Aires with a shock 2-0 victory in October.
"The rival on Tuesday is ourselves," the defender added. "We have to go out focused and we must not relax.
"We must go for victory because we lost three points against Ecuador and that cannot happen again."