The Colombian is on loan from the French Ligue 1 club, but has struggled to make a notable contribution since Jose Mourinho brought him in during the summer.
Falcao has not featured at all since the end of October due to a thigh injury, on which he underwent checks at Monaco’s training ground earlier this week.
Now Monaco believe he faces an extended spell out of action, meaning recalling him to the Stade Louis II would not be an appealing option.
Monaco vice-president Vadim Vasilyev said in an interview on the club’s DailyMotion page: “Falcao is currently injured. He has six to eight weeks to go like that. We have decided not to take him back to Monaco for the moment.”
Halfway through a season-long loan with Chelsea, the former Atletico Madrid striker has scored just one goal. He was similarly goal-shy while at Manchester United last season.
With Diego Costa and Loic Remy ahead of him in the pecking order, even a fit Falcao would appear unlikely to get much playing time with Chelsea for the rest of the season.
Press Association Sport understands Falcao recently rejected approaches from Mexican and Turkish clubs.
His contract with Monaco expires in 2018. Monaco signed the striker from Atletico in 2013 for £52million, but he spent just one season in Ligue 1, suffering a major knee injury midway through, before embarking on a disappointing loan spell at Old Trafford.