The Colombian international has been linked with a move to the Premier League - Chelsea and Manchester City are thought to be interested - while Real Madrid are thought to be keen on the striker.
But, according to Spanish newspaper El Economista and quoted on talkSPORT, the Stamford Bridge club are eager to tie up a deal for Falcao, and are even prepared to offer Courtois as part of the deal.
The Belgian international has spent the past 18 months on loan at the La Liga club, and has impressed with a number of composed performances at the Vicente Calderon.
The 20-year-old was bought by Chelsea from Genk in 2011, but immediately loaned to Atletico Madrid, as Petr Cech remains Chelsea number one.
And the report in Spain claims Chelsea are willing to offer £47m plus Courtois to land Falcao. Atletico are thought to be eager to keep Courtois for at least another season, and the Belgian may be open to a longer stay as Cech continues to block his path to the first-team at Stamford Bridge.
The former-Porto striker notched again at the weekend, as his side lost 2-1 to Rayo Vallecano.
The Colombian has 23 goals this season, a tally only Lionel Messi and Cristiano Ronaldo have bettered in Spain so far. Meanwhile, at Stamford Bridge Fernando Torres continues to struggle - he failed to find the net during Chelsea's 4-1 win over Wigan at the weekend - while Demba Ba sat out for the visit of the Lactics.
Falcao is widely regarded as one of the best strikers in world football, and a scramble for his signature is likely in the summer - even if Atletico hold on to a top four place and qualify for next season's Champions League.