The pair used companies in Belize, Britain, Switzerland and Uruguay to avoid paying taxes on 4.16 million euros of Messi's income earned from his image rights from 2007-09.
The decision means that the 21-month prison sentence has been swapped for a fine worth less than Messi's weekly wage.
According to El Mundo Deportivo, the five-time Ballon d'Or victor told the Catalans of his intentions in the same week as retiring from global duty with Argentina in the summer of 2016.
State prosecutor Isabel Lopez Riera told The Associated Press the fine-for-time deal was presented by Messi's lawyers to the judge who will rule on whether to suspend Messi's sentence as is widely expected.
Messi's case was one of the first high-profile investigations by Spanish authorities into top football players' tax affairs.
Mourinho reacts to allegations of tax evasion
Barcelona's Lionel Messi, Neymar and Javier Mascherano have also had issues with the authorities in the past few years. Barcelona's Lionel Messi was sentenced to a 21-month jail sentence and 2.09 million euro fine past year for tax fraud .
In the last two weeks, Real Madrid forward Cristiano Ronaldo and former Real Madrid coach Jose Mourinho have been accused by a Madrid-based state prosecutor of having defrauded Spain's Tax Office of millions of euros (dollars) in unpaid taxes.
Both have denied wrongdoing.
In the era of Messi "Barcelona" has won 30 trophies, including four wins in the Champions League and eight titles of champion of Spain.
Spain's state prosecutor would accept substituting a fine of 255,000 euros ($285,116) for the 21-month prison sentence handed down by a Barcelona court to soccer player Lionel Messi for tax fraud, Barcelona newspaper La Vanguardia reported on Friday.
The maximum fine would be €255,000, on top of a almost €2m fine paid by the 29-year-old as part of last year's sentence.
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