The U.S. Treasury Department will wait for General Motors Co’s first-quarter earnings before deciding whether to sell more of its investment in the nation’s largest automaker, a person familiar with the matter said.

The Treasury can sell some of its remaining 500 million GM shares, which equals 33 percent ownership, starting May 22, Bloomberg reported. Officials are waiting for GM’s earnings and to see what happens to the stock when bondholders in GM’s bankrupt predecessor company receive shares as partial compensation for their losses, said the person, who didn’t want to be identified because the plans aren’t public.

GM has dropped 20 percent this year in New York trading and 10 percent from its initial public offering price. While the Treasury may be willing to take a loss on the shares, which closed today at $29.59, the Obama administration is looking to sell at least in the range of the $33 IPO price, the person said. The government would need to sell the shares at about $53 apiece to break even on the investment.

“They will tell us when they’re getting out; I will not tell them when they’re getting out,” Dan Akerson, GM’s chief executive officer, told reporters today at an industry forum in New York. “There are many variables in their consideration and they don’t share that with us. They’ll notify us when they want to position for the sale.”

Mark Paustenbach, a Treasury spokesman, declined to comment. GM hasn’t said when it will report first-quarter earnings.

GM fell 38 cents, or 1.3 percent, to $29.59 at 4:15 p.m. in New York Stock Exchange composite trading. The shares slid as much as 2.7 percent earlier to the lowest price since the IPO in November.

The Treasury may file to sell shares with a traditional S-1 filing after a lockup period expires on May 22. The Securities and Exchange Commission would then review the offering like an IPO, which would delay the actual sale until June, the person said.

If the department waits until July 1, the government would be able to sell the shares with a less-thorough review and could get the offering started more quickly. In that case, the Treasury likely would wait until Detroit-based GM reports second-quarter earnings before selling more stock, delaying the sale until August, the person said.

The Treasury may make a third offering of shares in November or December and doesn’t need to sell all of the shares this year, the person said.

The department’s auto task-force members haven’t met with Treasury Secretary Timothy F. Geithner, who would decide on any GM share sale, to discuss the timing of a possible secondary offering, the person said.

The Treasury, which owned 61 percent of GM after its 2009 bailout of the automaker, sold shares equal to a 28 percent stake during the IPO. In a January interview, Ron Bloom, who was head of the Obama administration’s auto-industry task force at the time of the IPO, said the government wanted to sell its GM shares “as soon as practical.”