Spanish newspapers citing a ruling by a judge in Gava, near Barcelona, said the Argentine player's father Jorge Messi deposited the payment, which covers €4.1 million in unpaid taxes plus interest, with the court on August 14.
Court officials were not immediately reachable to confirm the reports.
Prosecutors accuse the two of defrauding the tax office of income related to the use of his image from 2006–2009.
The reports said that after the payment was made the judge spared the accused from being made to pay bail.
The court has ordered the 26-year-old player and his father to appear for questioning this month. The hearing had been set for September 17 but a scheduling clash may cause it to be postponed, media reported.
There is a possibility that Messi's father may assume full responsibility for the tax fraud, thus exonerating the Barça, Spain's El País reported.