The developments comes amid widespread speculation the prolific Atletico Madrid hitman is on the verge of joining the big-spending French club.
According to reports in Spain, Falcao is due on Monaco for negotiations ahead of what could be £50million move to the Principality club.
If the transfer does go through, then Falcao would follow in the footsteps of his former Porto team-mates Joao Moutinho and Rodriguez, who recently moved to Monaco for a combined fee of 70 million euros (£60million).
And Rodriguez, who also plays alongside Falcao with Colombia, is relishing the chance to play alongside the 27-year-old once more, telling Colombian newspaper El Tiempo: "Obviously (it's good). I've already played with him and now we're going to be together again, that's also going to be good.
"I'm proud to be with a friend, hopefully we can achieve great things."