A Spanish state prosecutor filed a fraud complaint on Wednesday alleging that Messi and his father Jorge avoided paying €4 million (Dh19.5m) in back taxes through illegal overseas tax havens.
Laporta told Cope radio he is "convinced that they have not committed any irregularity".
Laporta's presidency coincided with the period the complaint covers from 2006-09.
If found guilty and barring an out-of-court deal with the tax office, Messi and his father could face two to six years in jail, according to Professor Sandalio Gomez, a sports finance analyst at the IESE Business School.
"We are surprised," Messi said on his Facebook account, "because we have never committed any infringement. We have always fulfilled all our tax obligations, following the advice of our tax consultants who will take care of clarifying this situation."
The complaint, signed by prosecutor Raquel Amado, was submitted for trial at the courthouse in Gava, the upscale Barcelona suburb where the Argentina forward lives.
In it, Amado says from 2006-2009 Messi "obtained significant revenue derived from the transfer to third parties of his image rights, income which should have been taxed".
The complaint says Messi "circumvented his tax obligations" by using shell companies in tax havens such as Belize and Uruguay.
A judge at the courthouse must accept the prosecutor's complaint before charges can be brought against Messi and his father.
Messi had the day off on Wednesday after playing for his national team in Quito, where Argentina was held to a 1-1 tie with Ecuador on Tuesday night in a qualifying match for the World Cup.
Argentina coach Alejandro Sabella has said Messi was expected to be in the lineup for an exhibition against Guatemala on Friday.
Forbes rated Messi as the world's 10th highest-paid athlete. He reportedly earned US$41.3m (Dh150.5m) to June this year, with $20.3 coming from his club salary and $21 million in endorsements.
Messi signed a two-year contract extension with Barcelona in February that keeps him at the club through June 2018 - when he will be 31. He joined Barcelona when he was 13 and made his debut with the first team three years later.
The forward scored 60 goals in all competitions this season, leading Barcelona to the Spanish league title. With Messi struggling to recover from a leg injury, Barcelona was eliminated from the Uefa Champions League in the semi-finals.
Spain has been cracking down on tax evasion as it tries to repair the country's public finances amid the recession and collapse of its real estate sector.
Finance Minister Cristobal Montoro warned soccer players in April they should make sure they are "comfortable" with their tax affairs.
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