Fellow senior All Blacks Brodie Retallick and Sam Whitelock are also believed to be mulling this option, should it come to fruition.
Speaking ahead of the All Blacks' test against the Wallabies in Tokyo on Saturday, Barrett said Japan was an attractive option but he will make his decision when the time comes.
"There is a lot to like about Japan," he said at the All Blacks press conference in Tokyo.
"What I can say is there is good open communication with the coaches, my management and NZR and I am happy that at the right time I will make the right decision.
"I'll leave it at that for now. When the time is right it will be obvious and I'll make a decision."
New Zealand Rugby head of professional rugby Chris Lendrum confirmed to the Herald last week that talks about Japan in 2020 was something they were aware of.
"That concept of Japan 2020 comes up in a number of conversations," he said.
"Generally what we understand is they are looking to run two Top League seasons during 2020 but that's not confirmed.
"From a salary and welfare perspective that has obvious attraction for players who potentially have had long Super or international careers and are looking to refuel body, mind and wallet for maybe another few years."
Japan is yet to finalise its season structure beyond next year but the World Cup, which kicks off in September in Tokyo, has forced the 2019-20 domestic campaign to be pushed back to January the following year.
The Japanese Top League has already lured All Blacks Dan Carter, Israel Dagg, Matt Todd, Richard Kahui, Andy Ellis, Augustine Pulu and a host of other internationals.