The player agreed to pay 7.4 million euros and more than 790,000 euros in interest to reach an agreement on the fraud claims that dated back to 2012 and 2013, according to El Mundo which cited documents from the Spanish tax office.
The tax office and the player's agent Gestifute said on Thursday that they could not confirm the report.
Falcao was accused by Madrid's prosecutor of not properly declare about 5.6 million euros paid for image rights.
The prosecutor was not immediately available for comment.
Falcao's payment follows a string of similar cases in which soccer players have reached agreements with Spanish authorities over tax evasion charges related to their image rights.
Last week, a Spanish court swapped a 21-month prison sentence handed to soccer player Lionel Messi for tax fraud last July for a 250,000-euro fine.
Former Real Madrid player Angel Di Maria also reached an agreement over a tax evasion charge related to his image rights.
Meanwhile, Real Madrid player Cristiano Ronaldo has been called to testify on July 31 in Madrid on allegations that he hid income from tax authorities between 2011 and 2014. He denies any wrongdoing.
(Reporting by Jesús Aguado; Additional reporting by Paul E. Day and Raquel Castillo; Editing by Louise Ireland)
