Jose Mourinho's side are reportedly keen to sign another forward, and the Colombian could be the answer.
According to the Mail report, the forward’s loan spell at Old Trafford is rumoured to have cost them as much as £40m, comprising his £285,000-a-week wages and a £6m loan fee.
Dutch coach Van Gaal recently confirmed that his club would not be pushing ahead with a potential £44million deal for Falcao, although he reportedly would like to stay in England, rather than return to Ligue 1, and would be prepared to take a wage cut in order to seal any potential transfer.
Chelsea are keen to sign another striker as back up to Diego Costa - with Didier Drogba having left the club to continue his career elsewhere and Loic Remy failing to establish himself - while the Spain international has been out injured with a persistent hamstring injury.
Falcao’s agent, Jorge Mendes, is also Jose Mourinho’s agent, while he has also worked closely with Marina Granovskaia, who is the director responsible for all transfers at Stamford Bridge, making a deal all the more possible.
Whether the Blues could negotiate him down to an agreeable deal, though, remains to be seen.