Falcao missed Monaco's 2-0 win over Rennes on Saturday due to a thigh injury but although Ranieri did not confirm the Colombian striker will return for the principality club's next fixture, the Italian coach hinted his star forward is improving.
Despite not playing against Rennes, Falcao remains equal top of Ligue 1's goal-scoring charts with nine goals - level with Paris Saint-Germain pair Edinson Cavani and Zlatan Ibrahimovic.
"I do not know if Falcao will play on Tuesday," Ranieri said after the victory over Rennes.
"This morning he trained a little and the injury was more or less OK.
"Tomorrow morning he will train again and on Monday I will decide (whether he will play against Nantes)."
Saturday's game against Rennes was Monaco's second of three they will play in nine days.
Ranieri was impressed by how his players started strongly to gain control of the match with James Rodriguez and Anthony Martial both scoring in the first half, which allowed Monaco to cruise after the break.
"When you play three games in nine days, 2-0 is not a bad result," Ranieri said.
"What we have to do in this circumstance is keep the ball and take the game at your own tempo.
"We played very fast, as per the second half. It was a very good performance and result for us in a difficult match."
Thank you for reading 5 articles this month* Join now for unlimited access
Enjoy your first month for just £1 / $1 / €1
*Read 5 free articles per month without a subscription
Join now for unlimited access
Try first month for just £1 / $1 / €1