Kishida is expected to announce the new plan during a Green Transformation (GX) meeting of officials to be held later on Wednesday, the newspaper said, without citing sources.
The move would mark a turnaround for Japan, which has kept most of its nuclear reactors idled in the decade since a massive tsunami triggered a disaster at the Fukushima Daiichi power plant in 2011.
Public opinion had broadly opposed nuclear restarts following the Fukushima disaster, but the tide has shifted given rising fuel prices and a hot summer that have spurred calls for energy-saving.
Last month the government said it hoped to restart more nuclear reactors in time to avert any power crunch over the winter.
As of late July, Japan had seven operating reactors, with three others offline due to maintenance. Many others are still going through a relicensing process under stricter safety standards imposed after Fukushima.
Kishida is also expected to call for further restarts, domestic media said, as well as lengthening the amount of time existing plants will be allowed to remain operational before decommissioning given the long periods they have remained offline.