The 28-year-old was named in Jose Pekerman's provisional 30-man squad for the World Cup finals in Brazil but the Argentine coach has to decide by June 2 whether Falcao should be included in the final group of 23.
Falcao trained with Monaco on Friday for the first time since having knee surgery in January and promised he will only go to the World Cup if he can 'contribute'.
"To get to 100 per cent football-wise will be impossible, because I lack hours of competitive football," Spanish newspaper Marca quoted Falcao as saying.
"In order to resume, if I am feeling good, I will go.
"If I see that I am not sure, and I'm not going to contribute anything, I will be sensible and I will not go."
Falcao completed a low-intensity training session at the Stade Louis II with Monaco's coaching staff and appeared happy with his progress.
The session included passing drills, shooting and low-intensity competitive work, where Falcao received passes before spinning away from a defender.
"I'm getting better every week," the Colombian told Monaco's website.
"It (his left knee) evolved well and I'm happy about that. My knee is fine.
"I work in a simple manner every day. I am getting used to coordination with the ball."
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