"I spoke to him on the phone yesterday (Thursday)," said Ranieri at a press conference ahead of Sunday's top-of-the-table showdown in Ligue 1 against Paris Saint-Germain.
"He is calm. He is doing well and he will match the match against Paris on television. He is working hard and his rehabilitation is going fast. He can see that his knee is reacting well and he is very happy with that."
When asked if he thought Falcao, who turns 28 on Monday, might recover in time to go to the World Cup with his country, Ranieri replied: "I think he will be there."
He added: "It would be a miracle but he is very focused. Everything is going well for the moment. He is optimistic. But the second and third months will be very important."
Falcao ruptured the anterior cruciate ligament in his left knee during a 3-0 French Cup win against minnows Chasselay last month, but the surgeon who operated on him in Portugal later said that he felt the player had a "slim chance" of making the World Cup.
Monaco moved to replace Falcao in the January transfer window, recruiting Bulgarian striker Dimitar Berbatov from Fulham on a deal until the end of the season.
Ranieri has hinted that Berbatov could make his debut against PSG on Sunday night, while Jeremy Toulalan and Ricardo Carvalho are set to return after missing last weekend's 2-2 draw at Lorient due to suspension and a minor injury respectively.