The 29-year-old has made just 10 appearances since joining the Premier League champions last summer and is currently unable to train, with Jose Mourinho revealing in November that the striker has suffered “an important muscular injury”.
Vasilyev has now revealed that Monaco had assessed Falcao with a view to allowing him to return until the end of the season.
“It's true that we have spoken several times with Falcao,” Vasilyev told RMC.
“The first idea was that he returned to Monaco to play the second half of the season.
“He came to us, he was assessed by our doctors. Unfortunately, he was injured. We took the decision, it is better that he remains at Chelsea.”