The match would pit the Blue Samurai against a global squad featuring superstars such as Barcelona forward Lionel Messi and Real Madrid star striker Cristiano Ronaldo, the Nikkan Sports daily said.
The International Federation of Professional Footballers, known by its French abbreviation FIFPro, is arranging the date in cooperation with its Japan chapter, the daily said.
The Japan Pro-Footballers Association could not immediately confirm the report when contacted by AFP.
The March 11 disaster has left more than 26,000 dead or missing, and crippled a nuclear power plant northeast of Tokyo, sending radioactive material leaking into the air.
Japanese all-stars are due to play a charity match in Osaka next Tuesday with the Blue Samurai, who won a record fourth Asian Cup in January, facing a J-League select.