Le Pen's bank account with the HSBC bank's Swiss arm contained 2.2 million euros, 1.7 million of them in gold bars and coins, according to investigative website Mediapart.
In May 2014 the account was closed and transferred to an account in the private Swiss bank CBH in the Bahamas, the site says.
The accounts were run through a trust placed under the legal responsibility of his butler, Gérald Gérin, the report adds, basing itself on information received by prosecutors in Nanterre, near Paris, from the anti-money-laundering unit, Tracfin.
In 2013 Le Pen, who became a millionaire in the 1970s thanks to the legacy of a wealthy supporter, Hubert Lambert, admitted holding an account at UBS in Switzerland, which he opened in 1981.
His wife, Jany, closed another Swiss account in 2008.
The Front National founder, who is a Euro-MP, faces an investigation over undeclared assets estimated at 1.1 million euros.
He also has problems inside his own party, now led by his daughter Marine.
He is to appear before its executive committee on 4 May over remarks about the Nazi gas chambers and Marshall Philippe Pétain's collaborationist government during World War II.
Le Pen on Tuesday dismissed the charges as "part of the general offensive against us".
"This notification is going to be examined by prosecutor Catherine Denis and the financial division to decide whether to pursue judicial action," the prosecutor's office at Nanterre, near Paris, said later in the day.
Neither CBH nor HSBC have commented on the report.
Front National vice-president Florian Philippot, a close ally of Marine Le Pen, said he knew nothing about the Mediapart allegations.
"I don't know whether it's true, but knowing Jean-Marie Le Pen, I would find it strange if it were," Philippot said. "I've spoken to Marine Le Pen on the phone. She is very surprised and doesn't know anything about it either. Like the rest of us, she is waiting for Jean-Marie Le Pen to clarify and explain."