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French publication RugbyRama suggests Read will link up with Toyota Verblitz while Crotty will play for Kubota Spears in the Japan Top League.
France's daily sports newspaper L'Equipe also reported on Monday that Read would not be joining Paris club Racing 92 for the 2019-20 season and was now likely to join a Japanese club.
With the Rugby World Cup being hosted in Japan this year, the Top League will run two modified seasons in 2020, essentially offering a double payday to players.
The double-season leaves the potential for players to earn twice what can be made in Europe in the same 12 month period.
The Rugby Rama report claimed Racing 92 had targeted Crotty to strengthen its midfield, but then switched its sights to Read after hearing the All Blacks skipper might be available.
Racing had high hopes of signing Read after talks during the All Blacks' European tour last November despite competition from an unnamed English club and Japan, L'Equipe reported.
Read told the New Zealand Herald in November that he will bring down the curtain on his long and illustrious All Blacks career at the World Cup in Japan next year.
Read, who turned 33 last month, is almost certain he'll be taking up an overseas contract. What he has not sorted out yet is where he will be going.
Read and his wife Bridget have three young children and they have always wanted to have an overseas experience together.
They want to have it before their children get too far into their schooling and 2020 is seen as the perfect time.
By that stage Read will be 34 and have completed his third World Cup – having been part of the victorious teams in 2011 and 2015.
He'll have played close to 50 tests as captain, been World Player of the Year in 2013, won Super Rugby titles with the Crusaders and played in a British Lions series.