The Daily Star reports that the Blues could even offer Fernando Torres as bait in a deal to land Falcao this summer.
Torres has failed to make the expected impact at Stamford Bridge since joining Chelsea from Liverpool last year.
Chelsea have watched Falcao in action in almost every Atletico Madrid game for the last three months.
Chelsea boss Andre Villas-Boas worked with Falcao while both of them were at Porto.
Falcao has a £50million buy-out clause in his contract with Atletico Madrid.
