Jose Carlos Noronha admits that the odds are stacked against Monaco attacker but says it is not impossible for a player as athletic as the Colombian to recover in time.
The Colombian, 27, suffered cruciate ligament damage on Wednesday, and his injury means that an appearance in Brazil in the summer looked impossible.
However, though surgeon Jose Carlos Noronha admits that the odds are stacked against the former Atletico Madrid forward, he thinks that Falcao has a slight chance of making the international tournament's finals.
"It will be difficult. There are only five months before the tournament," the doctor said in an interview with RMC Sport. "Ideally we'd have seven or eight months in these cases, but we will see how the situation evolves.
"Falcao is a top athlete. He has a good physical condition so we can hope, even if we are aware that time will not play in our favor. He will give everything to recover. He has the mindset and the ability to get a good result. He still believes he can make the World Cup. He has not given up."
Colombia has been grouped with Cote d'Ivoire, Greece and Japan in this summer's World Cup.