The 37-year-old is ready to leave the Los Angeles Galaxy after their MLS Cup Final match this Saturday, with his lucrative contract set to expire.
Beckham is said to be looking for one last challenge before retiring from the game and has been linked with a move to the Australian A League or the financially tempting Chinese Super League.
Monaco could provide the midfielder with a short-term goal, having dropped from the top tier of French Football to Ligue 2 in 2010.
They have the economic muscle to lure ‘Becks’ to the Stade Louis II after being taken over by Russian billionaire Dmitry Rybolovlev last January.
Since then former Chelsea manager Caludio Ranieri has been drafted in as well as a number of talented young players such as ex-Arsenal starlet Nacer Barazite.
There is also the factor of the principality being a tax haven, which would allow Beckham to earn a vast deal of cash before the end of his career.
QPR manager Harry Redknapp is keen to bring the once England captain to London, but no official approach has been made.