The two nations are set to meet on Sunday for a place in the semi-finals, with both teams arriving at the stage after impressive performances in the Round of 16.
Argentina advanced after defeating Colombia, while Switzerland secured their quarter-final spot following a victory over Egypt.
Speaking during an appearance on ESPN FC, Leboeuf tipped Switzerland to overcome the South American giants after extra time, predicting a narrow 2-1 win for the European side.
“I’m going to go for Switzerland [to win] in extra-time. 2-1 win,” the former France international said.
Leboeuf’s prediction sets up the possibility of another major upset at the tournament, with Argentina entering the match as one of the favourites after lifting the World Cup trophy in Qatar four years ago.
The winner of the Argentina versus Switzerland tie will face either England or Norway in the semi-final, as teams continue their pursuit of a place in the World Cup final.
Argentina, led by a squad carrying the confidence of defending champions, will be aiming to continue their title defence, while Switzerland will look to create history by eliminating one of football’s strongest national teams.