Private equity firm KKR & Co. is exploring an offer for Toshiba Corp., according to a person familiar with the matter, in a move that could start a bidding war for the storied Japanese conglomerate.

KKR is weighing a bid that would be likely to value Toshiba above the $21 billion buyout proposal that it’s already received from CVC Capital Partners, said the person, who asked not to be identified as the details aren’t public. Canadian investment giant Brookfield Asset Management Inc. is also in the preliminarily stages of exploring an offer for the company, including how such a bid might be structured, a separate person with knowledge of the matter said.

The deliberations are at an early stage, no final decisions have been made, and the discussions may not lead to firm offers, the people said.

Toshiba confirmed on Wednesday that it had received a preliminary bid from CVC, and Bloomberg News later reported that the European firm is in talks with investors in Japan to join its offer — a move that could help win local regulatory approval for the deal. CVC is planning to provide new details on its takeover offer as early as this week, according to a person familiar with the matter.

Representatives for CVC, KKR and Brookfield declined to comment. U.S.-based representatives of Toshiba didn’t immediately respond to an e-mailed request for comment. The request was made during U.S. business hours.

Toshiba’s U.S.-traded shares surged as much as 13% Tuesday after the Financial Times earlier reported details of the possible bids.

An executive at the Japanese conglomerate, who asked not to be identified, has said that the private equity firm offered about 5,000 yen per share for Toshiba, which would value it at about 2.28 trillion yen ($20.9 billion). That price has already been deemed as too low by Oasis Management Co., a Hong-Kong-based hedge fund that’s been an investor in Toshiba since 2016.

Toshiba CEO Nobuaki Kurumatani, under pressure from investors and losing confidence from his own employees, is expected to step down, Nikkei reported separately on Tuesday. Chairman Satoshi Tsunakawa will succeed him as CEO, the newspaper said. Support for Kurumatani from Toshiba executives and other employees fell sharply in a recent internal survey, Bloomberg reported this week.