The papers -- released Sunday -- implicate several high-ranking government officials, including a member of FIFA's ethics committee as well as a number of prominent sport stars.
The more-than 11 million documents, which date back four decades, are allegedly connected to Panama law firm Mossack Fonseca. The International Consortium of Investigative Journalists (ICIJ), which published the 2.6 terabytes of leaked data, reports that the firm helped establish secret shell companies and offshore accounts for global power players.
CNN is unable to independently verify the reports and is seeking comment from the most prominent figures mentioned. They are spread across Europe, Asia, the Middle East, Africa and the Americas.
While owning an offshore account is not necessarily illegal, El Confidencial reports Messi, who is widely considered to be the world's best player, set up "a tax fraud network" by using Panama company Mega Star Enterprises to avoid paying tax on image rights deals. The Madrid-based newspaper was part of the ICIJ investigative team.
Documents posted online by the Spanish newspaper show both the signatures of Messi and his father, Jorge, in acquiring Mega Star.
Messi has been key to Barcelona's success over the past decade, and the club was quick to express its backing for its leading player.
"Since the very first moment that the 'Panama Papers' which accuse Leo Messi were released, FC Barcelona has sent its affection and support to the player and to his whole family," said Barcelona in a statement released Monday.
"The club makes all of its judicial means, fiscal and administrative, at the family's disposal in order to make his actions and honor clear in this case."
Meanwhile Messi has instructed his lawyers to "analyze the opening of legal proceedings against the media outlets that have published this story," as he described the accusations of "having created a new web of tax fraud and, even, money laundering" as "false and slanderous."
"In response to the news released by various media outlets in which Lionel Messi is attributed to the forming of a company with the aim of 'putting in place a new web of tax fraud', the Messi family wishes to make it clear that Lionel Messi has not carried out any of the actions he is accused of," said a statement sent to CNN by the Barcelona star's legal representatives.
"The Panamanian society to which this information refers to is a completely inactive company, which never had funds or open current accounts and that derives from the old corporate structure designed by the previous tax advisors of the Messi family, whose fiscal consequences for Lionel Messi were regularized in due time, declaring before the Spanish Tax Authority all the proceedings accrued from the exploitation of his image rights."
A spokesman for Spain's Tax Agency said: "We are analyzing all the information released to the public by several media outlets," referring to its investigation of Spanish residents named in the Panama Papers.
The spokesman declined to name any individuals, adding: "We have opened a probe into these allegations and we will use all of the means at the disposition of the Tax Agency to investigate them. This investigation is still in a very early stage."
Messi, and his father are due to appear in Spanish court in May or June for a separate case, in which the pair are accused of defrauding the tax office of almost $4.5 million.
In January, Messi -- who is set to play for Barcelona against Spanish rival Atletico Madrid in the Champions League Tuesday -- was crowned the world's best player as his won his fifth Ballon d'Or award.
Ramon Fonseca Mora, a co-founder of Mossack Fonseca, told CNN that the information published about the firm was false and full of inaccuracies.
In longer statements provided to the International Consortium of Investigative Journalists (ICIJ), the firm said that the parties "in many circumstances" cited by the ICIJ "are not and have never been clients of Mossack Fonseca."
The ICIJ carried out the yearlong investigation in cooperation with more than 100 different news organizations.