The Daily Star is reporting that the Stamford Bridge club have sent representatives to every Atletico game for the past three months.
The Blues want to reunite the Colombian striker with Andre Villas-Boas – manager during his time with Portuguese champions Porto.
The report also suggests that Chelsea are willing to offer £50million flop Fernando Torres as part of the deal.
Torres is adored in Madrid as he captained Atletico for a number of years before his big-money move to Liverpool.
Falcao broke the European scoring record in Porto’s Europa League winning-run last season – hitting 17 goals in just 14 games.
He has already found the net 17 times in 25 games for Los Rojiblancos this season and Chelsea want to bring his eye for goal to Stamford Bridge.
Torres has so far scored only five times for the Blues since he made his British transfer record move form the red side of Merseyside.