According to a Japanese media, Sony has its next flagship phone in the works and as anyone would expect, it's going to utilize the successor to the Snapdragon 855 and 855+. The first evidence of such SoC has surfaced on Sony's firmware distribution server.
The SoC has an internal model number SM8250 and it's widely believed that this is the chipset itself, for now, called Snapdragon 865. There's also a rumor going around that the chip will come out in two variants - with integrated 5G modem, like the recently launched Kirin 990, and one iteration with 4G connectivity.
It would make sense for Qualcomm to offer both models as 5G is still new to the scene and not everyone wants to pay extra to be an early adopter. It's not clear, however, whether Sony will offer its future flagship with both options, but it's safe to assume that it will. Judging by past Xperia releases, we will see the phone next year during the Mobile World Congress in Barcelona.
Source (in Japanese)