The Daily Express says Blues are ready to pull the plug on their £45 million move for Falcao.
Owner Roman Abramovich, who wants to bring in another striker in January to bolster Chelsea's Premier League and Champions League challenge, had earmarked Falcao, above, as his No1 target.
Abramovich is unwilling to pay that kind of money and has told Atletico he will not be held to ransom over Falcao, who has a buy-out clause in his contract set at £45m.
A source close to Abramovich said last night: "Roman is not sure about Falcao at the moment. Atletico are adamant they want their money back, and Chelsea will not pay that figure."