Fifa has said their disciplinary committee are currently "assessing the match reports" before deciding whether to "take steps" over the incident.
Following their late comeback to beat England 2-1 on Wednesday night, members of the Argentina squad celebrated with a banner that read "Las Malvinas son Argentinas", which translates as "The Falkland Islands are Argentinian".
The banner was held by Manchester United defender Lisandro Martinez, Tottenham Hotspur captain Cristian Romero and former Spurs star Giovani Lo Celso, now with La Liga club Real Betis.
Martinez and Romero are currently based in England.
On Thursday, Downing Street backed calls from other politicians and pundits for a Fifa probe into the behaviour of the defending World Cup champions.
Former England international Peter Reid described the Argentina banner display as "beyond the pale".
A Fifa spokesperson had said: "As is standard procedure, Fifa's independent disciplinary committee is currently assessing the match reports and considering the relevant circumstances before deciding on potential further steps based on the Fifa disciplinary code."
The Falkland Islands are a UK overseas territory, with islanders voting overwhelmingly to remain so in 2013.
In April 1982, Argentinian forces invaded the islands but were forced to surrender by June of the same year.
Argentina were fined by Fifa for holding up a banner with the same slogan after a friendly against Slovenia in 2024, while Spain players Rodri and Alvaro Morata were banned for one match each by European football's governing body Uefa after singing about their country's claim to Gibraltar after winning Euro 2024.
The display of political banners and statements are prohibited at all FIFA events in accordance with the rules of the global soccer body.
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