Mitsubishi Motors shares plunged more than 40% in the three days after the news emerged, their worst hat-trick of losses since the company listed in 1988.
The scandal has raised questions about the Japanese carmaker's future, after German giant Volkswagen posted its first loss in 20 years in 2015 because of the fallout from its own huge emissions-rigging scandal.
Mitsubishi Motors plans to offer to cover the extra fuel costs incurred by vehicle owners because their engines were less efficient than advertised, the Nikkei reported.
The move aims to "appease angry customers' nonstop inquiries" and prevent an "exodus" of buyers, the Japanese business daily said, without giving its sources.