The Colombia international striker has been on the books of Monaco since the summer of 2013 and has a contract until June 2018, according to Transfermarkt.co.uk.
The 30-year-old has been out on loan for the past two seasons, first at Manchester United and then at Chelsea.
Falcao played on loan for United from Monaco during the 2014-15 campaign and featured for Chelsea last season.
On June 24th I will start the pre-season with @asmonaco. I am excited and committed with the beginning of the trainings with the club.— Radamel Falcao (@FALCAO) 10 June 2016
It is quite interesting and somewhat bemusing, as Falcao has not been at his best for two years and could not make much impact in England.
The former FC Porto star scored four goals and created 18 chances in 26 Premier League matches for United during the 2014-15 campaign.
Falcao scored one goal and created two chances in 10 league appearances for Chelsea this past season.