The 17-year-old winger is already appearing for the Estudiantes first team in Argentina’s top flight.
Sarmiento is an Argentina youth international and scored four goals in six games for their under-16 side.
Any deal would likely see Sarmiento remain at Estudiantes for the time being due to his age.
Sarmiento is still a minor and doesn’t turn 18 until March next year, meaning he would not be able to get a work permit.
Estudiantes are likely to accept City’s offer because in the context of the Coronavirus crisis, it is a fortune for the club.
One of Argentina’s great young talents, Sarmiento has won praise from the likes of Juan Sebastian Veron and Alejandro Sabello.