The Argentine Football Association (AFA) had offered him an extension, but according to daily newspaper La Nacion’s website, Sabella “has told Julio Grondona (AFA president) that he won’t continue as coach”.
The 59-year-old took Argentina to the World Cup final in July, where they lost 1-0 to Germany after extra-time.
He had taken over from Sergio Batista after Argentina’s dire Copa America showing on home soil in 2011, where they reached only the quarter-finals.
An AFA spokesperson refused to comment on the reports to AFP, indicating only that Sabella will hold a press conference at the national team’s training centre in Ezeiza, near Buenos Aires, at 1900GMT on Wednesday.
Two days before the World Cup final Sabella’s agent said he would not extend his contract while the coach himself said he would only make a decision after the tournament in Brazil.
Several names have been touted by Argentine press as potential replacements, including former Barcelona coach Gerardo Martino, Colombia coach Jose Pekerman and current Atletico Madrid boss Diego Simeone.