Following Argentina's third consecutive final defeat, manager Gerardo Martino's future is in doubt.
Should Martino get sacked or step down as Argentina boss, many would like to see Diego Simeone manage the Copa America runners-up.
Diego Simeone also speculated after Atletico Madrid's Champions League final defeat to Real Madrid that he would consider his future at the Spanish club.
This could mean that Simeone would potentially consider managing his native country.
However, Atletico president, does not want the Argentinian FA to approach the 46-year-old.
"I said no to the AFA, they can do what they want," he explained.
In addition to this, it appears that Simeone would now like to continue at Vicente Calderon and was perhaps speaking in the heat of the moment after losing the Champions League final to rivals Real Madrid.
"I spoke heatedly, us Argentines are like this," Simeone said on Wednesday.
"The others do not take the blame for beating you, I learnt that with time. You have to remember the pain and suffering, because it is necessary to then get over it.
"I don't think there are many better teams than us," he added. "To be better than Atletico is hard, because we play as a team.
"At every corner of the club, it's now been four and a half years that we are constantly eager to improve," the Argentine said.