Western Union Co. is in early-stage talks to acquire smaller rival MoneyGram International Inc., people with knowledge of the matter said, as both companies contend with stiff competition from upstart money-transfer companies.

MoneyGram had a market value of just $415 million as of Tuesday’s close, though in an acquisition Western Union would also have to take on about $960 million of debt. Talks may still fall apart, said the people, asking not to be identified because the matter is private. MoneyGram shares surged 35 percent in afterhours trading.

Western Union and MoneyGram, the two dominant players in the remittance industry, are facing price competition as companies including WorldRemit, TransferWise and Walmart give their customers new options for moving cash. MoneyGram reported a loss of $72 million in the first quarter, compared with a profit of $39 million in the year-earlier period.

The company lost a key relationship with Wal-Mart in 2014 when the retailer decided to start its own money-transfer business. Dallas-based MoneyGram’s market value dropped by half in the three years through Monday.

Though Western Union has fared better, its shares are still well off highs seen before the global financial crisis. The Englewood, Colorado-based company has a market value of about $11 billion.

Representatives for Western Union and MoneyGram declined to comment.

One potential hurdle is whether regulators would block the deal on antitrust grounds, the people said. Winning approval would have been less feasible several years ago before the new competitors fragmented the once heavily consolidated remittance industry, they said.

MoneyGram, controlled by Thomas H. Lee Partners LP and Goldman Sachs Group Inc., explored a sale in 2013, drawing bids from Euronet Worldwide Inc., Carlyle Group LP and TGP Capital, Bloomberg News reported at the time. The company was also the target of an unsolicited offer from Euronet in 2007.

Thomas H. Lee and Goldman Sachs bought MoneyGram in 2008 in a deal valued at $1.65 billion including debt, outbidding Euronet.

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