The 29-year-old defender is not playing at Old Trafford and Estudiantes chairman and former United midfielder Juan Veron has convinced him the move away from Europe can boost his career.
Rojo wants to return this week and establish himself in the plans of coach and former teammate Gabriel Milito, says the Daily Mail.
Then he believes he can return to the Argentine national squad and play a part in the Copa America this summer.
Rojo saw a temporary move to Everton fall through on deadline day in August after United demanded a £4m loan fee.
He progressed through the youth system at Estudiantes, making 43 appearances for the club between 2008 and 2011, before joining Spartak Moscow.