Partial services for the gaming network as well as music service Qriocity will be available from Saturday morning, according to Famitsu (via VG247).
Countries expected to rejoin the service are Japan, Thailand, Taiwan, Singapore, Malaysia and Indonesia.
Last week, government authorities blocked the return of PlayStation Network in Japan, saying it had yet to fully disclose its security plans.
Services including online multiplayer were resumed for Europe, North America and other regions last week.
Sony has said that the PlayStation Store will return before the end of the month.
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