Two of the three proposals include buying shares at a discount to Uber’s valuation, but also provide a face-saving way for the company to maintain its $68.5 billion value. Dragoneer’s investment coalition wants to buy out shareholders at a discount to Uber’s current valuation, and SoftBank is offering to buy shares at a lower valuation as well. But both groups would also purchase a small amount of new shares at Uber’s current valuation to keep the company’s value propped up on paper.

The group led by Mr. Pishevar said it would purchase the shares at the current valuation. Whichever deal ultimately gets approved, this would be the first time that Uber has sold a large chunk of shares at a price that was the same on paper as a previous round of financing.

A spokesman for Uber and a spokeswoman for Uber’s board declined to comment, as did SoftBank and a spokeswoman for Mr. Pishevar. Dragoneer did not respond to a request for comment.

SoftBank emerged as one of the first to be interested in buying Uber shares. For months, the conglomerate has angled to purchase the shares from existing investors at a discount to the company’s current valuation. To let Uber preserve its $68.5 billion valuation on paper, SoftBank agreed to put a small amount of new money into the company at that price.

Uber’s board has been wary of the SoftBank proposal because of investments by its founder and chief executive, Masayoshi Son, in the ride-hailing company’s rivals in Asia. But Mr. Son and SoftBank could offer Uber strategic help in Southeast Asia, where the service has been spending heavily. The two sides have quietly worked for weeks to test whether there is enough interest from sellers to make a deal work.

More recently, an investor coalition led by Dragoneer, which includes the private equity firm General Atlantic and others, has emerged with a deal that would protect Uber’s valuation. The proposal incudes a small purchase of new shares at the current valuation, but the bulk of the investment would come through buying out existing shareholders at a discount via a so-called Dutch auction — an auction that begins with a high price that declines until a buyer says yes.