The La Liga side are preparing one final attempt to keep hold of their star player, and are reportedly ready to offer the Colombia international a huge new deal to extend his contract.
The 26-year-old is widely considered to be the best number nine in world football, and has begun the season in sparkling form.
His goal in Atletico Madrid's 3-1 victory over Osasuna on Sunday night took his total to 13 in nine appearances.
Chelsea are thought to be keen to sign Falcao, and the reports suggest the Stamford Bridge side are preparing a £38m bid for the former-Porto star for when the transfer window reopens in January.
Chelsea have only two senior strikers, Fernando Torres and Danny Sturridge, and have been linked with a move for another in January.
But Premier League champions Manchester City have also been credited with an interest in Falcao, and Roberto Mancini could rival Roberto Di Matteo for the striker when the window reopens.
City have plenty of options up front, including Edin Dzeko, Mario Balotelli, Carlos Tevez and Sergio Aguero, and a move for Falcao would likely result in one of those four leaving City.
But Atletico are thought to be ready to fight to keep hold of the Colomiban, and are eager to tie him down to a new deal, with the view to possibly extracting more money from any future transfer fee by virtue of a longer-term contract.
The report suggests the Spanish side are proposing to add an extra year to Falcao's contract, along with a bumper pay rise in order to secure his Atletico future.