Various German media reports have suggested that the Blues have already moved to acquire the Atletico Madrid striker on the request of 'incoming' Blues boss Jose Mourinho.
The talk has been supported by Sky Bet reporting a run of bets on Falcao heading to west London, prompting the odds on a move tumbling from 6/1 to 1/5.
The 27-year-old has scored 25 goals for Atletico this season to propel them to third in La Liga, just three points adrift of local rivals Real Madrid, but has a release clause of just over £50million in his contract.
Meanwhile, a return for the 'Special One' has appeared on the cards for some time, the former Stamford Bridge chief having repeatedly spoken of his desire to work in the Premier League again.
A return to Chelsea has been odds-on for over a month but further backing on Wednesday night, when Real Madrid's Champions League hopes were significantly dented with a 4-1 defeat to Borussia Dortmund, saw the price for a second stint at the Bridge cut to 2/7.
Sky Bet's Chris Spicer said: "It is difficult to decipher whether the backing is really from those in the know of just people buying into the reports, but the amount of stakes we have seen has certainly warranted a significant shift in odds.
"Manchester United were previously backed into favourites to sign Falcao following speculation in the Spanish media that a deal had been agreed, so it certainly would not be unprecedented for foreign media speculation followed by subsequent backing to prove misleading."