The reports said Sabella, whose side lost 1-0 to Germany in the final at Brazil's Maracana, had told Argentine FA (AFA) President Julio Grondona of his decision not to stay on.
If Sabella steps aside, the AFA will have to move quickly to name a successor with Argentina beginning preparations for their next major tournament, the 2015 Copa America in Chile, with a friendly against Germany in Duesseldorf on Sept. 3.
Former Paraguay and Barcelona coach Martino, and Pekerman, who steered Argentina to the 2006 quarter-finals and Colombia to the same stage in Brazil, are front runners to take over.
Sabella, 59, has called a news conference for Wednesday (1900 GMT) at AFA headquarters where he is likely to explain his decision and possibly reveal his future plans.
Sabella's agent, Eugenio Lopez, said two days before the World Cup final that the coach was unlikely to carry on and Sabella himself said on his return to Buenos Aires that he was unsure if he had the energy to give his best any longer.
"You have to fill the energy tank which sometimes gets empty. I have to think if I'm in condition to give 100 percent," Sabella told reporters two weeks ago.
Sabella, who took charge in August 2011, led Argentina to first place in the World Cup qualifiers where they scored 35 goals in 16 matches.
His side won their three group matches in Brazil, thanks mainly to four goals from Lionel Messi, and Argentina's progress through the knockout rounds to their first World Cup final in 24 years was marked more by sound tactics and a firm defence.
Argentina have further friendlies during a tour of Asia in October. They meet arch-rivals Brazil in China and also play against Hong Kong.
Martino and Pekerman have both worked with Messi.
Martino coached him at Barcelona last season, where he also had Argentina's midfield general Javier Mascherano in the team. He has World Cup experience as Paraguay coach in South Africa in 2010.
Pekerman handed Messi his first Argentina cap in 2005 and also gave him his World Cup finals debut in Germany the following year.