The Colombian striker, currently on international duty at the Copa America in Chile, scored four goals in 29 games on loan at Manchester United last season.
United turned down the opportunity to sign the former River Plate, Porto and Atlético Madrid forward on a permanent deal however Chelsea see the 29-year-old as the perfect replacement for Didier Drogba who was released by the club at the end of last season.
Chelsea will pay Monaco a reported loan fee of £7.2million for Falcao and £35million if they want to sign him at the end of the 2015/16 season.
Blues manager José Mourinho is a huge admirer of Falcao and attempted to sign him while managing Real Madrid and Falcao played for bitter rivals Atlético.
In a interview with DirecTV Sports last week, “The Special One” responded to the speculation of Falcao signing for Chelsea by saying: “If I can help Falcao reach his level again, I will do it.
“It hurts me that people in England think that the real Falcao is the one we saw at Manchester United”.
Before his time at Old Trafford Falcao had a fearsome reputation in front of goal (scoring 138 goals in 229 games) and will be determined to rebuild it at Stamford Bridge.