The two faced each other on the pitch on Wednesday night as Brazil drew with Colombia in a friendly in the United States.
Falcao has been linked with a January transfer window move from his club Atletico Madrid, for whom he has scored 10 goals this season.
With Fernando Torres still struggling to find the form he displayed during the peak period of his Liverpool career, Falcao could be just the player the Blues need to boost their Premier League title bid.
"He would fit perfectly in to the squad," Luiz said. "We would all be happy (if he signed) because Falcao would undoubtedly a great player for our team. He is very difficult to stop. He is an excellent striker."