The England number eight has been sidelined with a fractured arm since January, missing a dismal Six Nations campaign in which Eddie Jones’ surrendered their title and finished fifth.
Vunipola has endured an 18-month period to forget in terms of fitness and has undergone surgery on his knee and shoulder. As such McCall will not rush back the forward for the quarter-final tie.
“It's a little bit uncertain, Billy is in a race against time to be ready for the quarter-final,” McCall said.
“We'll make a call on what the surgeon says. If the arm isn't right to play then we won't risk him. He's been injured enough, we don't want to re-injure him.
“Billy is very close to coming back but whether he makes the quarter-final we're not sure yet.”