Reports have claimed the Barclays Premier League champions are poised to bring the Colombia international back to England following last season's unsuccessful stint with Manchester United.
Representatives of Chelsea were not available for comment when contacted by Press Association Sport.
The 29-year-old scored just four goals in 29 appearances for United and the club opted not to take up an option to sign the player on a permanent deal.
That recent record may not have put off Chelsea, who are on the lookout for a new forward following the departure of Didier Drogba.
Manager Jose Mourinho recently spoke of his admiration for the player - who boasted a prolific record prior to joining United - but there has been no confirmation from either club of a possible deal.
Falcao first shone in Europe with Porto, scoring 72 goals in two seasons
Another 70 followed in the proceeding two seasons after moving to Atletico Madrid
Monaco then splashed out £50million to secure his services in 2013 and United paid a £6million fee for their one-year loan, with an option to buy for a reported £43.5million, last summer.
However, returning from a serious knee injury that ruled him out of the 2014 World Cup, Falcao was unable to rediscover his best at Old Trafford.
Yet while United manager Louis van Gaal decided Falcao did not fit the bill, Mourinho spoke positively.
As a former Porto manager, Mourinho claimed an affinity with the player and said last week: "It really hurts me that people in England believe that Falcao is the guy they saw at Manchester United.
"He's a player I know, one that I've followed since Atletico Madrid and if I can help Falcao arrive at his level I will do it."
Falcao is currently at the Copa America in Chile with Colombia.
Source : PA
Source: PA