Chelsea have also joined Arsenal in the hunt for Newcastle United striker Demba Ba, who has a £7million release clause.
Granovskaia, who is a far more influential figure than her job title would suggest, has become personally involved in a number of deals that Chelsea have negotiated in the last couple of years.
Her presence in Madrid sparked speculation that Chelsea might attempt to bring back José Mourinho as their next manager, but that option is currently believed unlikely given that Abramovich is still smarting over the £18m pay-off received by the Portuguese when he left the club in 2007.
Falcao is a long-term target and is available for £48m - his buy-out clause. But Chelsea face strong competition from Manchester City and Real Madrid for the highly-rated Atlético Madrid striker, who netted five goals against Deportivo la Coruna in a 6-0 win last night.
City manager Roberto Mancini recently held talks with Falcao's agent, Jorge Mendes, but Real still appear to be favourites to acquire his services.
Higuain has also been a long-term Chelsea target and the prolific 24-year-old Argentinian has struggled to command a regular place at Real under Mourinho.
Ba, meanwhile, is determined not to renegotiate the buy-out clause in his contract because he is personally due £2.5m of the £7m fee, should it be triggered, and because he also knows that Newcastle will not meet his demands of £70,000 a week should he agree a new contract.
Arsenal are considering Schalke's Klaas-Jan Huntelaar as an alternative to Ba. Chelsea are also drawing up contingency plans should they fail to sign up Pep Guardiola as their next manager.
Borussia Dortmund coach Jurgen Klöpp and Germany coach Joachim Low are viable options, while a surprise candidate could be Wigan Athletic's Roberto Martínez, who is admired for the positive football his teams play.
Chelsea have arrived in Japan ahead of the Club World Cup and goalkeeper Petr Cech insists the tournament is not an unwanted distraction for the Blues.
They will take on Mexican side Monterrey in their semi-final in Yokohama on Thursday.
With two wins from their last two games, including Saturday's victory over Sunderland, Chelsea finally appear to be coming into form and, with the busy Christmas schedule just around the corner, the trip to Japan could be seen as coming at exactly the wrong time.
Cech, though, sees it differently.
"I'm very happy to be here," the 31-year-old said. "It means a lot for any player if you can play in such a great tournament. You only get your invitation when you win the Champions League, which isn't easy. I had to wait eight years to get the entry with Chelsea, so I hope we will make the most of it.
"Our last two results were very good, so we will try to carry that momentum into this tournament."