The Daily Star says the newly promoted team are currently at odds with French league bosses over a tax dispute.
Falcao is currently on a massive tax-free salary, which other Ligue 1 sides can't offer their players.
The deal bringing the 27-year-old to the Principality based outfit was worth £51m, and helped kick start their summer spending spree.
Monaco are reportedly facing a £75m fine if they fail to resolve the alleged dispute.
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