The Colombian international has also been a long-term for Manchester City, but Chelsea club executives, acting under the approval of Roman Abramovich, have confirmed their intention to activate the striker's €60m (£48.1m) release clause when the transfer window reopens in January.
And Goal.com reports Falcao has reciprocated the interest, making it clear that he is willing to discuss terms with Roberto Di Matteo's side.
Chelsea have reportedly made Falcao a contract offer, and the Colombian is thought to have agreed a deal in principle with the European champions that would make him one of the highest paid players in the Premier League.
Di Matteo currently has just two senior strikers to choose from, and neither has found the back of the net with any regularity this season.
£50m striker Fernando Torres has started this campaign in more impressive form than last season, and the Spaniard has scored seven goals in 18 appearances. But the former-Liverpool player still looks a shadow of the striker he once was, and the Blues - who sit top of the Premier League - may look to strengthen in January.
Danny Sturridge is the club's other recognised striker, but reports have suggested he could be on his way out in January.
The Goal.com report claims Torres will likely be put up for sale to help fund the purchase of Falcao - a striker who Chelsea are believed to view as a replacement for the Spain international.
Falcao joined Atletico Madrid from Porto in a £34.7m deal last year, and replaced Manchester City bound Sergio Aguero in the process. Since then, only Lionel Messi and Cristiano Ronaldo have scored more La Liga goals than the forward.
City were also thought to be interested in Falcao, but it now seems Chelsea are in pole position to land the frontman, which could spell the end for Torres at Stamford Bridge.