The Impact will face Real during their Canada tour.
Chelsea legend Drogba said: "I played against Cristiano in the 2008 Champions League final that Manchester United won. He's a real leader and he deserves to win the Ballon d'Or for his great performances both for Real Madrid and Portugal. Although he wasn't on the pitch at the final whistle, he was still the main reason why they got that far.
"For the Montreal Impact it's very significant that Real Madrid are training here, given the history of the club. It's important to see how such a major team go about their work. I've played against Real Madrid many times, with Marseille and Galatasaray and I've also lined up against Zidane. Real Madrid is a really great club and an extremely prestigious one. It's an honour to have them here."