Chelsea are looking to offload Romelu Lukaku this summer and use the money to buy another striker, the Daily Star say.
It is claimed that Atletico Madrid are interested in the 20-year-old Belgian, who is on a season-long loan at Everton.
Colombian striker Falcao, who has been repeatedly linked with a move to Stamford Bridge, only joined Monaco last summer and has just been sidelined by a serious knee injury.
Meanwhile, the Daily Mirror reports that Chelsea want defender Kurt Zouma but are struggling to agree a fee with St Etienne.
The French club reportedly want £18m, with Manchester United said also be interested but unwilling to meet the asking price.
St Etienne co-president Roland Romeyer is quoted as saying: “Some clubs have launched a bid for the player, but we will not change our strategy.
“There have been discussions for Zouma with English, Italian and French clubs, but he will not be leaving this month unless we find an agreement with some of the potential buyers.
“If not, he will have to wait until the summer. We are under no obligation to sell.”
Zouma, 19, is apparently keen to move to England.