Colombian Falcao, who scored two goals in his team's 5-3 defeat at the Etihad stadium in the first leg, sustained the injury last weekend in a Ligue 1 match.
He was back in training on Monday but failed a late fitness test for the game against City in Monaco in which Kylian Mbappe and Valere Germain will start up front for the hosts.
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(Reporting by Julien Pretot; Editing by Ed Osmond)
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