By Omar Abdel-Baqui and Alexander Saeedy 

Hertz Global Holdings Inc. said some of its stockholders are selling 37.1 million common shares, as the rental-car company seeks to start trading again on a major stock exchange.

The shares will be sold between $25 and $29 each and proceeds would go to stockholders selling them, not Hertz, the company said Wednesday in a regulatory filing.

The proposed sale of stock represents a large windfall to the investor group who helped fund Hertz's exit from chapter 11 in June, including Knighthead Capital Management LLC, Certares Opportunities LLC, and Apollo.

Hertz stock, which trades over the counter, fell 10% to $31.60 on Wednesday afternoon. The shares had more than doubled from August through Tuesday's close.

The rental-car company's stock has traded over the counter since it was delisted last year after the company went bankrupt. Hertz said Wednesday it has applied to list on the Nasdaq under the ticker symbol HTZ.

A Hertz representative wasn't immediately available for comment.

Hertz's stock price rose sharply after announcing last week a deal to buy 100,000 Teslas. Tesla Inc. Chief Executive Elon Musk cast doubt on the deal when he said late Monday on Twitter that a contract has yet to be signed with Hertz.

The car-rental company on Tuesday stood by its announcement and said Tesla deliveries have already begun, but a spokeswoman declined to say whether there was a contract between the two companies.

In the Wednesday filing, Hertz said Knighthead and Certares will own 37.2% of the company after the offering assuming the underwriters' option is exercised in full.

The two firms billed themselves as long-term investors in Hertz during the chapter 11 bankruptcy, when two competing groups of investors jockeyed to own the rental-car company in an auction process.

Hertz said it intends to buy between $250 million and $500 million of the common shares from the underwriters. It also said it intends to make an offer to purchase the company's outstanding $1.5 billion preferred stock, provided by Apollo, by the end of this year.

Goldman Sachs Group Inc., J.P. Morgan Securities, and Morgan Stanley are acting as lead bookrunning managers for the proposed offering, according to the Securities and Exchange Commission filing.

Write to Omar Abdel-Baqui at omar.abdel-baqui@wsj.com and Alexander Saeedy at alexander.saeedy@wsj.com