Fourteen-time Major winner Woods is not sure to feature at Celtic Manor in October, having withdrawn from the game indefinitely following revelations about his infidelity.
"A lot depends on whether Tiger plays as he hasn't lost in the singles," said Montgomerie. "But if our 12 play to their potential, with the crowd's backing, we will win."
The Scot added: "Nobody is quite sure how long this absence [of Woods] is going to be. We hope he gets back playing and winning tournaments as soon as possible.
"He will come back, but whether he will retain that mystique as an iconic player, I'm not sure. It will be tougher for him."