"Batista is more out than in," the national news agency Telam quoted an AFA executive committee member as saying, while broadaster C5N said: "His days are numbered."
The media speculated that Batista, whom the AFA confirmed as being safe for now only last Monday, had lost the support of committee members and forecast a decision would be made Monday in advance of an official announcement Tuesday.
The committee will meet Monday afternoon in Buenos Aires.
Batista himself took to the media to defend himself.
"I am sure of my footballing ideas and how to translate them on to the pitch. I always said the Copa was all about getting ready for the World Cup in 2014," he said in a letter to Clarin newspaper.
"I recognise there were mistakes (at the Copa) and I am prepared to correct them. I am absolutely resolved to keep going.
"The Copa was not in vain," he insisted, adding that "when changes had to be made I made them."
Batista was vilified in the press for not seeming to know his best team - he chopped and changed after a poor start before Carlos Tevez, whom he dropped after two games, returned to miss the decisive spotkick against Uruguay.
Should Batista be fired names in the frame to succeed him are Paraguay coach Gerardo Martino and also Alejandro Sabella, who as a player had brief stints with Sheffield United and Leeds and who is set to take charge of Al Jazira in the United Arab Emirates.
Sabella won the Copa Libertadores with Estudiantes two years ago.
Batista said he could understand the widespread disappointment after the team exited the Copa on home soil after a quarter-final shootout loss to old rivals Uruguay, who will now take on Paraguay in Sunday's final.
"I understand this pain, which is genuine and not ill-meant, as we did not deliver the goods," Batista wrote.
Humberto Grondona, AFA sub-director of team affairs at the Argentine Football Association and the son of AFA president Julio Grondona, said Monday the organisation would keep faith in the man who only officially replaced Diego Maradona six months ago.
There will be no "brusque changes - we never thought of going down that road," Humberto Grondona said, indicating that Batista would steer the team through the 2014 World Cup qualifiers from October.
Maradona, dumped after last summer's World Cup quarter-final thumping by Germany, was also criticised for using too many players but in any case had a poor relationship with Grondona senior.
Maradona himself bitterly criticised Batista in an interview, saying Tuesday he would not dare show his face after the Copa exit, adding that "if I had only beaten Costa Rica (Argentina's sole Copa success) I would have gone of my own accord."
Maradona and Batista were teammates in the side which won the 1986 World Cup.
Argentina's next scheduled match is a friendly on August 10 against Romania in Bucharest. In early September they will face Copa giantkillers Venezuela in a gala match in India then take on Nigeria in Bangladesh on September 6.
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