The 59-year-old guided his nation to the World Cup final in Brazil this summer, where they lost 1-0 to Germany, and has decided not continue as national team boss.
Widespread reports in the Argentine media claim the 59-year-old has informed the nation's football association of his desire to quit on the back of its World Cup final defeat to Germany this summer.
Just two weeks ago Sabella admitted he was unsure whether he had the necessary motivation to continue in his position.
“You have to fill the energy tank, which sometimes gets empty. I have to think if I’m in condition to give 100 percent," he said.
Argentina will have to move quickly to fill the hot steat given it has a friendly with Germany on September 3, as preparations begin for Copa America 2015.
Former Barcelona boss Martino, who quit Camp Nou at the end of the season, is the frontrunner to replace Sabella, while Colombia boss Jose Pekerman has also been touted as a leading contender.
Sabella was appointed in August 2011, with his exit bringing to an end a three-year spell in charge of Argentina.