Japanese media reported on Wednesday that the Tokyo district court has ordered the 64-year-old Franco-Brazilian businessman be held for a further 10 days.
Prosecutors are stepping up their investigation over allegations that Ghosn under-reported his pay by about five billion yen ($44.5 million).
Public broadcaster NHK reported that Nissan had paid "huge sums" to provide Ghosn with luxury homes in Beirut, Rio de Janeiro, Paris and Amsterdam "without any legitimate business reason."
Following his arrest on Monday they had 48 hours to either press formal charges, release him or request a 10-day custody extension to continue the probe.
Nissan's board will decide Thursday whether to remove him as chairman.
If he is removed it would be a huge reversal of fortune for the once-revered manager, creator of the three-way alliance (Nissan, Renault, Japan Inc.) which together sells more cars worldwide than any other automaker.
Shock on the streets of Tokyo
Ghosn was admired in Japan for turning Nissan around. But RFI's correspondent Frédéric Charles found many people were deeply shocked by his alleged fraud.
“He’s such a unique leader, he believes in globalisation and turned Nissan into a global enterprise,” office worker Hiroko Ito told RFI. “But this scandal is shocking.”
A former Hitachi executive described Ghosn as "greedy, ready to do anything for his own personal gain, he’s an able businessman but did everything to get rich. It’s repulsive.”
Renault sticking by its CEO, for now
Renault said it was sticking with the fallen manager as chief executive but has named chief operating officer Thierry Bollore as deputy CEO.
"This leadership guarantees the correct functioning of the Renault company," French Economy Minister Bruno Le Maire told media on Wednesday, adding that Renault’s leadership was “solid, but provisional”.
Le Maire is to meet his Japanese counterpart on Thursday to discuss “prolonging” the alliance.
Fall-out from the arrest
Paris and Tokyo have been scrambling to contain the fall-out from the arrest.
The scandal is the latest in a string to affect Japan Inc. and has wiped millions off the stock value of all three companies.
Nissan bounced back marginally on the Tokyo stocks exchange, after plunging following Ghosn's arrest.