John Crombez, Belgium's minister for fraud prevention, said any information on local "mailbox companies" held by France's richest man should be shared with Paris, newspaper De Tijd reported on Saturday.
Belgian legal and government officials did not immediately return calls seeking comment. LVMH said in a statement that its Belgian companies complied with all applicable laws.
Arnault, 63, caused an outcry in France earlier this year when it emerged that he was seeking Belgian citizenship, while insisting that the move was not tax-related.
Other wealthy figures, including actor Gerard Depardieu, have blamed France's high tax rates and recent increases for their decisions to leave the country. Soon after taking office in May, Socialist President Francois Hollande introduced a new 75 percent rate on income above 1 million euros ($1.3 million).
According to L'Echo, a Belgian daily, Arnault's holdings in the country include several companies registered at the same Brussels address with combined assets of 7 billion euros.
"If Bernard Arnault is working with pure mailbox companies in Belgium we should signal this to French tax authorities," the anti-fraud minister was quoted as saying.
LVMH said it was "surprised" by the press reports and denied any wrongdoing.
"The companies of Groupe Arnault and LVMH have very real economic activities in Belgium, where some of them have been based for several decades," the company said in an emailed statement.
"All of their activities are fully compliant with Belgian tax legislation as well as international law."
($1 = 0.7590 euros)
(Reporting by Laurence Frost and Barbara Lewis; Editing by John Stonestreet)
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