Radamel Falcao's surgeon Jose Carlos Noronha has revealed that the striker could be ready to play by the end of May.
The Colombia international injured knee ligaments early in the New Year playing for Monaco and had surgery in late January.
The recovery can take anywhere from four to six months, but that time-scale has been crucial to Falcao and his hopes of playing in his first World Cup finals this summer.
Six months out would mean Falcao could not play in Brazil, but four months' recovery time, as is now the hope, would mean he would be ready for the tournament.
Talking to Portuguese station Radio Renascenca, Noronha stated: "If the magnetic resonance imaging shows a darker aspect of the new ligament and an absence of inflammatory process around it, we will be able to let Falcao go on the pitch at the end of week 12.
"He could then resume jogging without big changing of direction or rough acceleration.
"Then, from the fourth month, he could be completely ready to play on the pitch, so would be ready for June 14 [Colombia's opening World Cup match with Greece]."