The Colombian moved to the Stade Louis II from Atletico Madrid earlier this summer for £55m after scoring 28 goals in La Liga last season.
However, Falcao insists that he and Ibrahimovic, who netted 30 times for Paris Saint-Germain last term, don't have a rivalry with one another.
"There are no duels between players," Falcao told L'Equipe. "Battles exist between teams, although, on a personal level, knowing that you are going to face some of the best players in the world is always a motivation.
"They're the kind of games everyone wants to win. I'm not going to play against Ibrahimovic, I'm going to face PSG."
Monaco are in action on Sunday when they face league leaders Marseille.