Western Union (WU 1.42%) is reportedly courting MoneyGram International (MGI) in a takeover bid that would combine two of the largest money-transfer companies in the U.S.

Bloomberg first reported the rumors, citing an anonymous source, who said Western Union has made an offer, but that the target company has not yet decided on its response. News of the potential acquisition sent shares of both companies higher. 

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Such an acquisition would remove Western Union's chief direct competitor in the U.S. money-transfer space at a time when it faces other threats to its business from digital payments companies such as Paypal (PYPL 0.64%). Bloomberg also reported that traditional money-transfer companies are facing increased regulation, as well as a persistent and growing desire among government officials around the world to legislate cuts to money transfer fees. 

A leader in global payment services, most of Western Union's business involves money transfers from one consumer to another,  collecting fees on every transaction. A large portion of those are international transfers -- the company operates in more than 200 countries and territories.

MoneyGram similarly makes most of its revenue through money transfer and bill payment, but says it primarily serves unbanked and underbanked customers who have less access to traditional financial services. It had more than $877 million in debt at the end of the first quarter after reporting a net loss of $21.5 million, which was more than the $13.5 million loss the company reported in Q1 2019.

The coronavirus pandemic has not helped MoneyGram either. Like other payments businesses, it reported an 18% drop in global money transfer transactions between March 15 and the end of March on a year-over-year basis.

As of the close of trading Wednesday, Western Union had a market cap of roughly $9.47 billion, while MoneyGram's was about $213 million.