Such a step would be a devastating psychological blow to the National Front as it struggles to come to terms with its failures in the April and June elections and the changed political landscape of the Sarkozy era.
M. Le Pen, 79, already faces deep internal dissent as he approaches a party conference next month which will be asked to extend his leadership for another three years. Last week, one of the party's own Euro MPs – and biggest creditors – placed a legal hold on the future of the party headquarters overlooking the river Seine at Saint Cloud, west of Paris.
For more than 20 years, the National Front has been the most successful far-right and xenophobic party in any large country in western Europe. With the arrival of President Nicolas Sarkozy's brand of populist, but largely moderate, right-wing politics, its electoral appeal has been severely squeezed.
The party's finances have been plunged deeply into the red by its poor performances in the presidential and, above all, the parliamentary polls earlier this year. The NF took out large loans to finance its campaigns, expecting to repay them from state subsidies.
The size of public subsidies to political parties in France depends mostly on the percentage of votes cast in parliamentary elections. The NF share of the vote slumped to 4.29 per cent nationwide, compared to 11.3 per cent in 2002 and nearly 15 per cent in 1997.
In a radio interview yesterday, M. Le Pen said that electoral failure had "cost" his party between ¿10m (£6.9m) and ¿12m. The National Front was "not bankrupt" but was "in a severe financial crisis". If the party could not raise new loans or reschedule its debts, he said, it would "perhaps be obliged to sell" its prestigious, modern office block in Saint Cloud.
These offices, known as le paquebot (the steamship), because of their vaguely nautical look, are worth up to ¿20m. When purchased in 1994, the paquebot was a symbol of the upward mobility of a party which had risen from nowhere to challenge the alleged "corrupt" stranglehold of the left-right elite.
A distress sale would foreshadow the end of the Le Pen era – and according to some internal critics – the possible disintegration of the National Front itself.
In recent weeks, a slow-motion leadership struggle has begun for the succession to M. Le Pen. He will seek, and win, another three-year term as party president next month but even the indestructible M. Le Pen has publicly admitted that this may be the last lap of a 60-year political career.
He has let it be known, for the first time, that he would like to be succeeded by his daughter, Marine, 39. This has angered the hard-line xenophobic and the ultra-conservative Catholic wings of the NF. They place the blame for their electoral reverses largely on Marine Le Pen's attempts to remould the NF as a softer, more modern, nationalist party open to young professional people and even to different races. They complain that this allowed Nicolas Sarkozy to seize, almost without opposition, some of the NF's most successful themes: national pride, traditional moral values and a hard-line on crime and immigration.
The party's former secretary-general Carl Lang has announced that he will not challenge M. Le Pen for the leadership next month but has said that he will challenge Marine Le Pen in three years' time.
In the meantime, he warned, M. Le Pen must make room in the party hierarchy for hardliners like himself. "If not, the process of uniting the different elements of the French national right will happen elsewhere."