Globalstar, the Covington-based satellite phone company, has filed applications to have its common stock listed again on the Nasdaq or the New York Stock Exchange.

Shares of Globalstar had been listed on the Nasdaq until December 2012, when the stock was delisted because the price fell below $1. At that time, the stock was trading at 30 cents a share. Since then, the company has traded as an “over-the-counter” stock, which means shares are traded through a dealer network rather than a centralized exchange.

But Globalstar has rebounded, closing Monday at $2.36 a share.

“We are pleased to be in a position to list on one of these two prestigious exchanges in the near future,” said Jay Monroe, chairman and CEO of Globalstar. “Our stockholders want enhanced trading liquidity and market visibility, and we look forward to completing this process as soon as possible in order to meet their requests.”

The improvement in Globalstar’s share price is largely due to the company’s completion of its next-generation satellite network, which cleared up problems with unreliable two-way communications. The company also cleaned up its subordinated and structured debt, lining up new financing.

“It was a difficult couple of years while we were waiting for the satellites to be delivered,” said Tim Taylor, Globalstar’s vice president of finance. “But our core satellite network has been restored and revenue is growing again.”

The company has petitioned the Federal Communications Commission to allow it to open up its spectrum to allow for wireless Internet service in American cities. By tapping the spectrum set aside for Globalstar in areas where satellite phone service isn’t needed — such as major U.S. cities and airports — the company has said it could increase Wi-Fi capacity in the U.S. by one-third immediately.

Globalstar officials have said the company has had discussions with “numerous” technology, wireless and cable companies about the spectrum. Bloomberg has reported that Amazon tested a new wireless service on a spectrum owned by Globalstar.

Taylor said Globalstar should be listed on the stock exchanges because of its $2.5 billion equity value. That’s based on the worth of the core satellite network and the wireless spectrum.

Globalstar said it meets all eligibility requirements of the New York Stock Exchange MKT and Nasdaq Capital Market, which list the stocks of small growth companies, with one exception. The Nasdaq requires that a stock close over $2 a share for 90 consecutive trading days.

“We’re on day 17 right now,” Taylor said. Once that 90 day mark is met, the stock listing is a “fait accompli,” he said.

Listing on the New York Stock Exchange is an interactive process that will involve a couple of months of back and forth.

“With a company our size and the cleanup we’ve done, we should hear something about eligibility in the first half of the year,” Taylor said.

The company expects to hear something about its stock listing in the first half of 2014.

Peter Ricchiuti, a finance professor at Tulane University who tracks regional stocks across the South through the university’s Burkenroad Reports, said while it may cost Globalstar more to be listed on the Nasdaq or NYSE because of regulatory filings, it’s worth it for the exposure. “Institutional investors buy these stocks,” he said. In contrast, over-the-counter stocks, also known as “pink sheets” because of the paper that printed the prices, have a taint to them.

“It’s kind of like the island of misfit toys,” Ricchiuti said.

The fact that Globalstar was delisted shouldn’t hurt the company’s application to be listed on the Nasdaq or NYSE, he said.

“People understand sometimes you have to take some time away from the spotlight and get your act together,” he said.