Grondona, known as "The Godfather," has headed AFA since 1979. He said in a radio interview on Tuesday that he "is tired," but wants to stay in the job for two more years to maintain his powerful position in FIFA.
"If I didn't have a mandate until 2015, I'd leave now," he said in an interview with Radio 10. "I feel perfectly fine, and I have to go on. I have a very important position with AFA and if I resign Argentina would lose a powerful position on FIFA."
Since Grondona has been in charge, Argentina has won the World Cup in 1986 and lost the final in 1990. But the national side has been disappointing in recent years, and Grondona has taken some of the blame.
He has never been far from controversy.
Critics have blamed him for the endemic fan violence in Argentine football, where every club match faces the threat of violence by hooligan groups. Grondona has said the problem simply reflects the growing violence on the streets of the country.
He has also been heavily criticized by former national coach and retired star Diego Maradona, who blamed Grondona for many of the festering problems in the national game.
Grondona hired Maradona as the national team coach and then dismissed him after Argentina lost in the quarterfinals of the 2010 World Cup.
"Here Don Julio (Grondona) does what he wants, and if they don't realize he's doing a bad job, what can I do?" Maradona said a year ago. "God help them."