The Colombian striker is currently out of action with a knee injury that has caused him to miss the World Cup - but that hasn't quelled speculation over his future. Having arrived at Monaco for £51 million from Atletico Madrid last year, Falcao failed to fully settle at his new club, and managed nine goals in 17 league games before his injury.
That, plus the suggestion that he's not happy in the principality has prompted rumours that he could be on the move this summer, and now Le10 Sport claim that Monaco are willing to sell up.
The Ligue 1 side appointed former Sporting Lisbon coach Leonardo Jardim recently, and according to Le10 he doesn't believe Falcao is the right man to lead the line next season.
That will be music to the ears of Chelsea fans, who will hope to see 'El Tigre' strut his stuff at Stamford Bridge next season. The Blues were heavily linked with him before his switch to Monaco and look short of options in attack despite the imminent arrival of Diego Costa from Atletico Madrid.
The biggest issue could be his price tag however. Chelsea have started to change their approach in recent transfer windows by spending less on players - or buying big when they can offset it against the sale of one of their players.
That's what happened with Cesc Fabregas and Diego Costa heading towards Chelsea - David Luiz has been sold to almost cover both players' fees.
However given that Moncao would in all likelihood look to recuperate the vast majority of the £51 million they paid for him almost 12 months ago, Chelsea may struggle to justify that sort of outlay.
That could in turn open the door for Real Madrid to swoop for the forward. Los Blancos have been linked with Liverpool's Luis Saurez but could view Falcao as a slightly cheaper alternative, while Alvaro Morata could also be part of the deal.
Arsenal have also been credited with an interest in the 28-year-old, but although they desperately need a striker, Falcao may not be the man for the job.