Reports in Italian newspaper La Gazzetta dello Sport, and quoted on news site tuttomercado.com, suggest Roberto Mancini is prepared to offload the Bosnian striker to sweeten the deal for the La Liga side.
But, Mancini travelled to Spain last weekend reportedly to scout Falcao, who scored as Atletico beat Malaga 2-1.
The 26-year-old has eight La Liga goals already this season, the same amount as Barcelona superstar Lionel Messi and Real Madrid forward Cristiano Ronaldo, and the Colombia international wants to beat the two Ballon d'Or contenders to the Pichichi this year.
Chelsea are thought to be leading the chase to sign the striker, and Roberto Di Matteo is believed to be considering his options before making a January bid.
The Atletico chairman said earlier this week Falcao could be sold for €60m, a fee that would help to reduce the club's debts.
Chelsea and Manchester City are one of the few clubs in the world that would be able to afford such a price, along with French side Paris St Germain.
Manchester City have also been linked with Fiorentina striker Stevan Jovetic, and Serie 'A' champions Juventus have recently pulled out of the race to sign the Montenegrin, paving the way for a possible City bid in January.
But according to the Italian reports, City will look to use Dzeko as bait to try and beat Chelsea to the signing of one of football's most in-form strikers.
Do YOU want to write for GiveMeSport? Get started today by signing-up and submitting an article HERE: https://www.givemesport.com/writeforgms