The Colombia international, who is on a season-long loan from French outfit Monaco, has missed the Red Devils’ last four fixtures with a calf complaint.
However, with the 28-year-old ruled out of country’s upcoming friendlies against the USA and Slovenia, rumours have emerged which claim he has not yet recovered from a long-standing knee problem.
Falcao took to social networking site Twitter to dispel the rumours, saying: “One fool speculates. A few others lacking objectivity respond and millions believe lies.
“It is disastrous what a few fools can do.”
Falcao missed Colombia’s World Cup campaign due to the knee injury he suffered at the midway point in the 2013/14 campaign.
He has made just four appearances for United since making the loan switch from Monaco, scoring one goal in the process.