ESPN understands Chelsea considered a move for Napoli forward Edinson Cavani but were priced out of a transfer.
• Cavani agrees extension
Chelsea were thought to be in the market for a striker during the transfer window, and Cavani was mentioned as a potential target.
However, Napoli's asking price of around £40 million for the Uruguay international prevented a deal being struck, and ultimately he signed a new contract at Stadio San Paolo.
A source told ESPN: "The name of Cavani was mentioned as a possible transfer at Chelsea, but not Falcao."
Chelsea were also linked with an approach for Falcao, who scored an impressive brace for Atletico Madrid in their 4-1 win over the Blues in the UEFA Super Cup.
But ESPN understands no bid was made for the striker, nor is there a £35 million deal in place to bring him to Stamford Bridge in the future.