UAR president Carlos Araujo confirmed the talks during his visit to Australia this week for a meeting of the southern hemisphere Sanzar body which runs the Rugby Championship.
"To take this match to London is something very important for the UAR and Argentine rugby," Araujo was quoted as saying by the UAR.
"That our national team could be the home team at that magnificent stadium speaks of the recognition they have and the great standing they currently have in world rugby."
The Pumas, whose match with Australia is scheduled for Oct. 8 in Argentina on the Rugby Championship calendar, last played at Twickenham when they beat the Barbarians 49-31 in November.
They also played their Rugby World Cup semi-final against the Wallabies at Twickenham in October, a 29-15 defeat.
Argentina and Australia will likely stay on for their tours of Europe in November. They both meet Wales in Cardiff in their opening matches, the Wallabies on Nov. 5 and the Pumas the following Saturday.