The Daily Star says both parties are confident a deal will be done that will see the Stamford Bridge side land one of Europe's deadliest strikers.
The final deal for long-term target Falcao, 27, is expected to be worth in the region of £40m although Chelsea could pay considerably less up front.
Chelsea could also boost their chances by allowing Thibaut Courtois to extend his stay at Atletico. The keeper has spent the last two seasons on loan at Atletico after joining Chelsea from Genk in 2011.
Can Falcao transform Chelsea into a title contender? Give us your shout below...