The ex-Blaugrana boss could be the successor to Alejandro Sabella, who stepped down despite leading the Albiceleste to this summer's World Cup final.
Martino left Camp Nou following a disappointing 2013-14 season that saw Barca miss out on the Primera Division title and fail to reach the semifinals of the Champions League for the first time since 2007.
But Martino could be named as Alejandro Sabella’s successor, according to AFA general secretary Miguel Silva.
“Our first candidate is Martino. If we agree with the economic issue and the agreements that everyone seeks, Martino will be the new coach,” Silva said. “We have one outstanding point, and we'll either agree or we will not agree.”
Sabella quit as coach of the Albiceleste following the national team’s 1-0 defeat to Germany in July’s World Cup final, and Martino was set to replace him before AFA president Julio Grondona’s death July 30.
Luis Segura was confirmed Wednesday as Grondona’s replacement, paving the way for talks with Martino to be completed.