The company said it has been providing information to Japanese prosecutors and is cooperating fully with their investigation.
Nissan's board of directors was treading a delicate balance between the apparent Ghosn faction of four members - including Ghosn himself - and five Japanese members.
The scandal was a "negative outcome of the long regime of Mr Ghosn", he said.
The extent of the misconduct allegations, or the arrest charges, were unclear as of Monday morning.
The revelation came after Nissan said Monday in a statement it has found "significant acts of misconduct" by Ghosn, such as "personal use of company assets".
Ghosn had been criticized for his salary of about $9 million ー exorbitant by Japanese standards.
Japanese media reported that Ghosn, who is also chairman and chief executive of Nissan's French partner Renault and one of the best known figures in the global vehicle industry, had been arrested.
Nissan's chief executive Hiroto Saikawa planned to propose to its board that Mr Ghosn and Mr Kelly both be removed from their posts, the company said in a statement.
Renault which is aligned with Nissan is a large employer in France
Kelly was also arrested on November 19 on suspicion of conspiring with Ghosn to under-report the Nissan chairman's income on annual securities reports.
He said that because of the continuing investigation, he could not disclose many details.
A Japanese judicial source told AFP that Ghosn could legally be held for up to 23 days but would possibly be freed on bail before then.
Companies in the alliance own parts of each other and share investments in new technologies, among other things. Management, including Saikawa, was strongly alarmed by moves for the two companies to completely integrate their management in keeping with the French government's intentions, and nervously watched every step Ghosn made. Ghosn was reportedly arrested by Japanese authorities Monday.
"Ghosn seems to be built for the job: He has the ability to connect with strangers instantly and to compartmentalize, no discernible private life outside his family, and a willingness to travel 300,000 miles a year (that's 11 circumnavigations)".
But he went on to add that the French state, as a Renault shareholder, "will be extremely vigilant to the stability of the alliance and the group". But he promised Nissan's leadership would get more involved in supervising top company officials.
Mr Ghosn joined Nissan in 1999 after Renault bought a controlling stake and became its CEO in 2001, remaining in that post until a year ago. In 2016, he also became chairman of Mitsubishi Motors, another one of Japan's large carmakers.
Born in Brazil, Ghosn joined French carmaker Renault in 1996 before he assumed the title of chief operating officer for Nissan in 1999.