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Shares of Visa were trading up about 5 percent around 3 p.m. ET. Visa declined to comment to CNBC on the reports.
The talks are reported to have began when Visa approached Visa Europe but could still fall apart if a price agreement is not reached. Price discussions range from $15 billion to $20 billion, according to Bloomberg, and both companies are working with advisors.
Visa Europe is a separate company from Visa, with a different corporate design. In October 2007, Visa Europe became independent of the new global Visa. At that time, Visa listed on the New York Stock Exchange, becoming a publicly traded company.
According to the Visa Europe website, the company is a membership association of European members and other payment service providers that have collectively issued more than 460 million Visa debit, credit, commercial and prepaid cards in Europe.
The company reports that those cards were used to make purchases and withdrawals worth 1.8 trillion euros (about $2 trillion) in the 12 months ending in June 2012.