Evacuation advisories have been issued in Kochi, as well as prefectures in Shikoku and Kyushu, Xinhua news agency quoted the Japan Meteorological Agency (JMA) as saying.
A level-4 advisory alert has been issued for more than 270,000 households.
According to the JMA, as of Thursday morning, Krosa was situated 60 km west of Cape Ashizuri in Kochi Prefecture.
Krosa is moving in a northward direction, the agency said, and will likely cut a path through western Japan on Thursday.
While the agency said the typhoon has weakened over the past few days, downpours of over 1,200 mm and violent winds have still been forecast for some eastern and western regions that are facing the Pacific Ocean.
Krosa has already severely affected transportation systems, with 673 domestic flights for Thursday cancelled.
More flights mighnt be cancelled henceforth, some carriers said, depending on the typhoon's trajectory.
West Japan Railway Co. announced Wednesday it would suspend the majority of its Shinkansen bullet train services on Thursday.
Shinkansen services between Tokyo and Shin-Osaka will also be operating at a limited service, Central Japan Railway Co. said, and Kyushu Railway Co. has announced it will reduce the number of its super-express bullet train services on Thursday.
Shikoku Railway Co. will completely halt operations on the western main island on Thursday, it said.
( With inputs from IANS )