The Blues are thought to be closing in on a deal for Villas-Boas as a replacement for Carlo Ancelotti at Stamford Bridge.
The Portuguese is thought to be weighing up the offer from Chelsea after Roman Abramovich made the 33-year-old his top target to become the club's new manager.
Reports have suggested Villas-Boas would make Falcao one of his top transfer targets if he does accept the Chelsea job and the Colombian's agent, Claudio Mossi, admits the player would be interested in a switch.
"If Villas-Boas is the new coach of Chelsea it is normal for players that are closest to follow him," Mossi is quoted as saying in The Sun.
The likes of Tottenham and Arsenal have been linked with Falcao in the past with the striker regarded as one of the best players in Europe after netting a record 17 goals in last season's Europa League campaign.
Source: Team Talk
Source: Team Talk