AFA has been warned that the potential name change for the Clausura championship, second of two tournaments in the season, which began last weekend, could breach FIFA statutes.
However, an AFA spokesman said the championship had not been given that name and the issue would probably be discussed at the body's weekly executive committee meeting late on Tuesday.
FIFA earlier issued a statement on the matter.
"FIFA contacted the Argentine FA (AFA) with regards to a potential change of name of the Liga de Primera Division. According to media reports, the league was set to be named after 'Crucero General Belgrano'," said FIFA.
"FIFA has requested the AFA to provide further information on this matter, and reminded the AFA of article three of the FIFA statutes which prohibits any kind of discrimination against a country, private person or group of people on account of ethnic origin, gender, language, religion, politics or any other reason.
It added: "A potential change of name of the Liga de Primera Division would clearly infringe the above mentioned article and could be sanctioned in accordance with the FIFA Statutes."
The AFA spokesman said: "How is it that the press don't analyse the logic [of the situation]? The idea arose legitimately from the broadcaster Futbol Para Todos. There is no note making a request to the AFA, but the executive committee only meets today.
"It will likely deal with the subject in accordance and in harmony with the demands and regulations of FIFA as a body affiliated to FIFA."
The sinking of the General Belgrano killed 323 Argentine sailors in what was a turning point in the war.
Tensions between Britain and Argentina have been stirred again in recent months by oil exploration in the Falklands. Britain's decision to send one of its most sophisticated warships to the islands has also reopened old wounds, though a new armed conflict seems unthinkable.
At present, AFA's website simply refers to the championship as "Torneo de Primera."
But reporters on Futbol Para Todos, the television broadcaster run by President Cristina Fernandez de Kirchner's government, referred to the championship as the Crucero Manuel Belgrano during matches at the weekend.
