The technical issues, found at nearly all of the European Union's 143 nuclear facilities, would cost about $32.2 billion to fix, the BBC reported Tuesday.
The final version of the leaked draft is due to be released Thursday.
"On the basis of the stress test results practically all [nuclear plants] need to undergo safety improvements," said the leaked draft, the wording of which could change. "Hundreds of technical upgrade measures have already been identified.
A number of safety measures were agreed to following the accidents at nuclear reactors at Three Mile Island and Chernobyl, the draft notes, but stress tests show the measures are still not implemented by some member EU states.
Specific failings were found at all 58 nuclear reactors in France, which relies on nuclear power for 80 percent of its electricity.
The report found power plants in the United Kingdom had no alternative emergency control room should the main one be contaminated by radiation.
Since the Fukushima disaster in March 2011, Germany has decided to replace nuclear energy with green technology and cleaner gas- and coal-powered plants by 2022.