White revealed to the Pretoria News that he was considering De Villiers for the No 10 jersey for the match in Buenos Aires on November 5.
"There is nothing to stop me from playing Jean at flyhalf against Argentina," he said.
White has been forced to consider his options at No 10 due to Jaco van der Westhuyzen having been ruled out of the tour with a knee injury.
The obvious concern of the move will be whether he has the kicking game to be successful in the position.
"There is a lot more to the game than kicking," countered White, who is also tempted to give Wayne Julies a run at inside centre if he moves De Villiers closer to the forwards.
"Wayne was the man of the match (in a recent Currie Cup game). He has played 10 Tests and won 10."
White is hoping that Mendez will agree to assist the Boks.
"It's an area where we can use his experience. Argentina are well known for their scrumming and he has played in all three positions in the front row," said the Bok coach.
"There is room for improvement in our scrumming. Federico has also played in the northern hemisphere."