It happened in the US a few months ago, and now something similar is about to happen in Japan, too: in one of Apple’s biggest markets, mobile carrier SoftBank is reportedly about to lose its exclusive domestic distribution rights for the iPhone and has to share the market with competitor KDDI.

Nikkei Business Online claims it has learned that KDDI au, Japan’s second biggest mobile carrier with 33 million customers, will provide the iPhone 5 starting next year. If the rumored roll-out of the phone next month will become reality in Japan, too, this means that SoftBank has a few months before its closest competitor can start tapping into their most important segment.

SoftBank has been Apple’s partner in Japan since August 2008 (when the iPhone 3G made its debut in Japan) and is also the exclusive provider of the iPad in this country. Gartner estimates that Apple, via SoftBank, has sold 7.5 million iPhones so far in Japan.

Nikkei Business also says the iPhone 5 will support the CDMA standard. Japan’s biggest mobile carrier NTT Docomo, long rumored to be interested in distributing the handset as well, will apparently be left out.

Neither Apple nor KDDI have confirmed the Nikkei Business report so far.