The safety standards relate to disaster preparedness by nuclear power plant operators. A draft of the standards prepared last month by Japan's Nuclear Regulation Authority requires operators to take broad measures against natural disasters and accidents.
The operators in the newspaper survey said the final cost to comply with the standards could rise as they cannot accurately estimate the expenses because parts of the standards are yet to be determined.
Since the March 2011 earthquake and tsunami disaster that crippled the Fukushima Daiichi nuclear plant, 48 of Japan's 50 nuclear reactors have been idled.
The Asahi Shimbun said the reactors can't be restarted until utilities comply with the safety standards, which are expected to go into effect in July.
The newspaper said the companies in its survey estimated the costs at $10.87 billion for 15 plants, which don't include the Fukushima plant.
The report said the estimates mainly cover expenses for emergency safety measures, such as construction of levees to guard against tsunami, and provisions for emergency power supply vehicles.
One utility said it needs to restart its idle reactors soon to improve its financial performance.