The Rugby Football Union has received a request from the Union Argentina de Rugby to hold the first test of next June's two game series in England for financial reasons.
The RFU are keen to help Argentina and are currently evaluating the stadium options for such a match.
RFU Chief Executive Francis Baron said: "Argentina feel that playing one of their two tests against England in England would generate urgently needed funds to invest in their squads, in particular the Pumas A team due to take part in the Churchill Cup in North America at the same time.
"We are keen to assist Argentina and will take the opportunity of playing the match away from Twickenham to aid rugby development in the regions."
Any change to the tour schedule must be approved by the International Rugby Board.