The company’s chairman – who also heads its alliance with Renault and Mitsubishi – was arrested in Tokyo on Monday after a private jet flight to be told he faced a series of accusations relating to his pay and use of company funds.
The Kyodo news service reported on Wednesday that officials had been granted extra time to question the global automotive executive.
Nissan claims an internal inquiry, initiated by a whistleblower, found he failed to disclose £34.5m of income with the help of another director, who also remains in custody.
That was allegedly achieved, local news reports suggested, through the use of a scheme to hide or share pay.
The company has also accused him of misusing money that belonged to Nissan.
That allegation is believed to relate, in part at least, to his ownership of homes in four countries.
Nissan has said Mr Ghosn will be formally sacked at a board meeting due to be held on Thursday.
There is also growing speculation that the company itself could form part of the police investigation.
It has already admitted its corporate governance fell short, given the power across the group held by Mr Ghosn.
He and Greg Kelly, the other executive detained, have not yet had a public opportunity to respond to the company’s findings.
The Financial Times has reported that the internal investigation had been taking place against a backdrop of full merger talks between Nissan and Renault.
The French brand’s board decided on Tuesday evening to retain Mr Ghosn as its chief executive and chairman, despite pressure from the French government – a major shareholder – to get rid of him.
Mitsubishi is expected to follow Nissan’s path by removing him as its chairman.
The scandal has prompted market talk of an end to the three-way partnership between Nissan, Mitsubishi and Renault – contributing to share prices declines of recent days.
The agreement sees them share costs and technology across brands and models but Masahiro Akita, auto analyst with Credit Suisse, told the AP news agency: “It’s not realistic to think the alliance will suddenly change as it is now already operating.
“You can’t go back on it that easily,” he said.