Falcao tore the anterior cruciate ligament in his left knee in January and looked set to miss this year's tournament in Brazil.
However, since undergoing an operation, Falcao has gained confidence that he could still play some part in football's biggest event, revealing that he would now be travelling to Spain to continue his treatment.
"I hope that I can play in the World Cup, but it's still too soon to be certain," he is quoted as saying by Sky Sports.
"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."
Falcao scored nine goals in qualifying, helping Colombia to their first World Cup since 1998.
‘He instantly popped into our ratings as one of the best U21 midfielders in Europe. The impressive thing is Slot has made him into more of a no.6' Inside Ryan Gravenberch's transformation at Liverpool
‘I don’t think Liverpool would look at Ollie Watkins, a striker isn’t a pressing issue for them – it’s Arsenal who need one’ Former Reds star explains why his old club don’t need an out-and-out forward this summer
