While the relationship has not been a particularly stormy one, the Verizon Wireless joint venture between Verizon Communications Inc. (NYSE: VZ) and Vodafone Group plc (NASDAQ: VOD) has been the subject of lots of conjecture over the past couple of years. Now Bloomberg is reporting that the two have been talking about ways to end the relationship either through a buyout by Verizon or a merger between the two companies.

Citing “people familiar with the situation,” Bloomberg reports that talks were held as recently as last December regarding a full merger, but the discussion dissolved when the two companies could not agree on management or a location for the corporate headquarters. That leaves a Verizon buyout as a likely alternative, provided of course that the U.S. telecom giant can finance the $115 billion price tag that Vodafone’s 45% stake in Verizon Wireless is said to be worth.

Vodafone has said that it would like to sell stakes in businesses that it does not fully own. Last year it sold its stake in a French mobile-phone operator and it sold a minority stake in China Mobile Ltd. (NYSE: CHL) in 2010.

Shares of Vodafone are up nearly 4% at $26.34 in a 52-week range of $24.42 to $30.07. Verizon’s shares are up about 1% at $47.54 in a 52-week range of $36.80 to $48.77.

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