Japanese construction firm Maeda Corp, which owns 24.68% of the roadbuilder, made an offer last week to boost its stake to 51%, which Maeda Road rejected on Friday.
"We have been in touch with potential bidders which are mostly private equity firms," said President Ryozo Imaeda. "A white knight is one of the options that we are considering."
Hostile takeovers have been rare in Japan as they were considered culturally taboo but they are slowly gaining acceptance as shareholders demand higher returns in a sluggish domestic market.
Last year, little-known Japanese hotelier Unizo Holdings Co attracted interest from U.S. private equity firm Blackstone and activist investor Elliott Asset Management, among others, after travel agent H.I.S Co launched a hostile bid.
Maeda Road shares surged to 3,835 yen after the bid from 2,633 yen before but have since drifted lower to close at 3,620 yen on Wednesday - still 37% higher than the pre-offer price.
Maeda Corp's offer of 3,950 yen a share, which runs until March 4, values the company's equity at 325.6 billion yen ($3 billion).
The bid appears to have come out of long-running discussions between the two firms about Maeda Corp's stake. Minutes before the hostile bid on Jan. 20, Maeda Road announced it had offered to buy out its biggest shareholder but did not name a price.
Imaeda told Reuters that protecting employees was a key condition in its search for a white knight and that he did not want a potential owner to sell company assets either.
Imaeda, who has been at the company for 43 years, also highlighted strategic differences between the two Maedas.
Maeda Corp, which makes most of its money in construction and civil engineering, is seeking to diversify into other areas such as operating highways through a government concession.
Maeda Road, meanwhile, remained focused on its core business, Imaeda said.
"If we become their consolidated unit, they can force us to do anything they want," said Imaeda.
A Maeda Corp spokesman said the company wanted to continue discussions with Maeda Road on how they could try to boost corporate value together.
By Junko Fujita and Ritsuko Shimizu