The 28-year-old has been out of action since rupturing cruciate knee ligaments while playing for his club in January.
"I hope that I can play in the World Cup, but it's still too soon to be certain," BBC Sport quotes Falcao as saying.
"I'm recovering quickly. Physiotherapy is going very well. 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."
Falcao has scored 20 goals in 51 international appearances.