The AS Monaco striker ruptured cruciate ligaments during a French Cup tie against lower league side Monts d'Or Azergues Foot on January 22 and underwent surgery in Porto three days later.
And speaking at the Stade Louis II stadium on Sunday, where he watched his side defeat Nantes 3-1, the 28-year-old revealed he is refusing to give up on his World Cup dream.
"I hope that I can play in the World Cup, but it's still too soon to be certain," Falcao said.
"I'm recovering quickly. Physiotherapy is going very well. I'm going to return to Spain to continue my recovery. The knee has responded very well, which allowed me to gain momentum in the work.
"I'm happy because the evolution is very positive. I'm a little ahead of what was expected, but we know very well that it's day to day that we'll see the evolution. I have the desire and motivation to return."
Monaco remain second in Ligue 1 with the win over Nantes and remain on course to qualify for next season's Champions League.
"I'm delighted for Monaco, we keep winning," he said. "The win was very important. We're still on track to achieve our objective of Champions League qualification. I hope to play Champions League with Monaco next season."
Colombia are drawn in Group C at the World Cup with Ivory Coast, Greece and Japan.