It is mainly a problem in the north of the North Island, but isolated infestations can be found as far south as Queenstown.
The EPA was calling for submissions so it could consider all views about the potential risks and benefits of introducing the two insects, Dr Fiona Thomson-Carter, general manager hazardous substances and new organisms, said last week.
"The wasps lay their eggs into the stems of the giant reed, which causes a growth, or gall that stunts, and sometimes kills the stem. The scale insects suck nutrients from the stem, reducing its growth rate," she added.
The reed was thought to be native to Eurasia, and although once valued as an ornamental plant, it was now an environmental weed in a number of countries.
The wasp and arundo scale had been released successfully in the USA and Mexico, where they were beginning to have an impact.
The NRC's application was made under the Hazardous Substances and New Organisms (HSNO) Act 1996, submissions closing on November 3.
A public hearing may be held before a decision is made.