Falcao has called Monaco home since arriving from LaLiga outfit Atletico Madrid in 2013.
The Colombia international helped Monaco to Ligue 1 glory in 2016-17, while he has scored more than 80 goals across all competitions for the French club.
Falcao, who spent time away on loan at Manchester United and Chelsea in 2014-15 and 2015-16, scored 16 goals for Monaco last season.