"This is the first time we have received a formal offer to construct roads since Nitish Kumar became chief minister nearly five months ago," an official told.
The government is likely to float tenders for a highway between Vaishali and Muzaffarpur districts in north Bihar in May, said an official of the state road construction department.
When a tender was floated for the Rs.4 billion project in 2004, no private bidder applied for it.
Government officials admitted that private construction companies were not willing to take up the project due to a perception that Bihar was India's most lawless state.
Jha's offer came after Nitish Kumar invited private companies to construct roads on a "build, operate and transfer" (BOT) basis.
Jha has submitted his bid to the government on behalf of a Mumbai-based private company to convert the 47 km Hajipur-Muzaffarpur highway into a four-lane super expressway.
Jha had earlier announced his plan to build several multiplexes in Patna, after the government announced a three-year tax rebate to private investors who set up multiplexes in the state. The government has already allotted land for multiplexes.
Jha, who hails from a village near Bettiah, campaigned for Nitish Kumar's Janata Dal-United during the state assembly polls in 2005