Falcao suffered anterior cruciate ligament damage during Monaco's Coupe de France tie against Monts Or Azergues on January 22 and went under the knife soon after.
The recovery time for a serious ACL injury is typically between six and nine months, which would rule Falcao out of the World Cup finals, but the 28-year-old is refusing to give up his dream of being in Brazil just yet.
However, Falcao is also staying realistic about his chances of being involved.
Asked if it would be a miracle for him to be involved in the finals, he told Marca: "It would be a special case.
"We are very optimistic about the response of the knee, but today is very premature to say whether or not I'm going to be at the World Cup. There are lots of days from now until the final decision."
Colombia supporters would love to see the prolific hitman involved in Brazil, but Falcao insists his main concern at present is just getting back to full fitness.
He said: "I'm doing everything possible to go, I would give it everything and it would be ideal, but the first thing is to be well, to recover well.
"I cannot allow that my desire and that of my country to be in Brazil to affect the state of my knee."
Regarding his rehabilitation, the former Atletico Madrid and Porto striker said: "I feel very good, the response from the knee in the first phase of the recuperation has been positive. There hasn't been any problem and this has allowed me to work well. The healing has been quick.
"It's been a day to day process. Some days are good, others less good, with more monotonous work.
"It's helped me a lot to have gone through the same injury some years ago, when I was at River Plate. Now I'm more relaxed, confident and calm."