The finer details were being discussed last night, with Monaco keen on taking Mario Pasalic or Charly Musonda on loan in return.
Falcao, 29, is with Colombia at the Copa America in Chile, preparing to face Brazil tomorrow.
Manchester United rejected the chance to sign the striker for £43.2m after a loan spell last season produced four goals in 29 games.
However, Jose Mourinho believes he can rekindle Falcao, saying: ‘It hurts me that people in England think the real Falcao is the one we saw at Manchester United. If I can help Falcao reach his level again, I will do it.’
Falcao’s arrival will prompt Loic Remy to consider his future at Stamford Bridge.
The 28-year-old is a target for West Ham and Crystal Palace but Chelsea would want close to £20m for the France international.
Meanwhile, Mourinho is playing hardball with Arsenal over their attempts to secure an £11m move for Petr Cech.
The Gunners want a deal for the Chelsea goalkeeper tied up this week, but are facing strong opposition from Mourinho.
Cech wants to join and it is understood Chelsea owner Roman Abramovich will not stand in the 33-year-old’s way.
However, Mourinho does not want to strengthen a rival by allowing Cech to move across London. The Chelsea boss has asked the Gunners for either Alex Oxlade-Chamberlain or Theo Walcott in return for Cech — but Arsene Wenger has rejected that proposal.
Mourinho would much prefer Cech to join Paris Saint-Germain, who are also interested. Nevertheless, Arsenal — knowing Abramovich has given Cech his blessing — are still confident of landing their man.
Mourinho’s reluctance to sanction Cech’s switch to the Emirates Stadium also stems from the lack of a ready-made replacement for the keeper.
Cech would leave Chelsea without a proven second-choice goalkeeper, something Mourinho is acutely aware of.
Stoke’s Asmir Begovic interests Chelsea, but the Bosnian does not want to be a No 2. QPR’s Rob Green is also a possible replacement. – Daily Mail
Original source: Chelsea closing in on Falcao