Citing reports from Spanish TV station Punto Pelota, the report claims Chelsea held discussions with Atletico to thrash out terms for an agreement between the two clubs.
The two parties are reportedly £5m apart at the moment, and negotiations have included discussions relating to Chelsea's on-loan goalkeeper Thibaut Courtois.
But the Stamford Bridge club are keen to keep hold of their highly-rated young shot-stopper, who's spent the past 18 months on loan at the Vicente Calderon, and have put a £17m asking price on the 20-year-old.
Falcao is the third top scorer in La Liga, behind Leo Messi and Cristiano Ronaldo, and he's widely regarded as one of the best strikers in the world.
His 21 goals in 28 games so far have helped Atletico Madrid to third place in the league, and they look well placed to qualify for the Champions League.
But the Colombian international may seek a move away from the Calderon regardless - he's been linked with a move for the past six months.
A January transfer failed to materialise, but speculation has continued to mount regarding a summer switch.