The Colombian striker signed for the newly-promoted Ligue 1 club in the summer from Atletico Madrid for €45m (£38m), but the newspaper claims the player considers himself let down by the Monaco hierarchy, led by wealthy Russian owner Dmitry Rybolovlev, and feels he has been recruited under false pretences.
As a result, he is looking for a way out of the French outfit and it is alleged the first club he was offered to was Madrid, who were interested in him when Jose Mourinho was in charge at the Santiago Bernabeu.
However, Los Blancos president Florentino Perez turned the proposal down as he felt the deal to bring Gareth Bale to the Madrid capital is too far down the line.
Falcao’s problems in the Principality have not been helped by his €14m (11.9m)-a-year salary possibly being halved due to tax changes proposed by Francois Hollande’s government.
Rybolovlev, meanwhile, is understood to have pulled the plug on any more additions to Claudio Ranieri’s squad in the wake of Ligue 1’s determination to force Monaco players into paying the country’s top rate of income tax.
It is a situation that has seen Monaco capture Ricardo Carvalho and Eric Abidal on free transfers and secure loan deals for Fabinho and Sampdoria goalkeeper Sergio Romero.
At present, Monaco players benefit from the special tax-free conditions that apply in the principality.
Carlo Ancelotti has admitted that Fabio Coentrao has asked to leave the club this summer.
The Portugal international has been heavily linked with a move away from Santiago Bernabeu, having been rumoured as a possible make-weight in the Gareth Bale deal.
And the Italian coach has confirmed that the defender wants to leave the club.
“The situation hasn't changed, apart from with Coentrao's position,” he told a press conference.
“Coentrao has asked to leave and he won't play tomorrow. Apart from him, I think the rest of the players here want to be here.”
Espanyol defender Hector Moreno has denied reports that he could make a move to Rubin Kazan this summer.
The Mexico international has been linked with a move to Russia in recent weeks, but the 25-year-old has insisted the rumours aren’t true.
“Nobody has talked to me about this,” he told reporters. “I just learned about it through the Press.
“It has never crossed my mind to play in Russia.
“It is not a distraction for me. I am preparing well with Espanyol.
“This club has given me a lot, and has allowed me to grow as a player and as a person.”