RNZ reports the union has tabled its final deals for Ben Smith, Israel Dagg and Aaron Cruden, and says it will give them the time they need to make a decision.
The trio's contracts end after the British and Irish Lions tour in June and all three have received lucrative offers to join French clubs.
While conceding New Zealand Rugby would never be able to match the big money bids from overseas, NZR chief executive Steve Tew said they had done all they could to retain the services of the three key backs.
"They all are key retention targets for us, they've all got final offers, they've all had in-depth conversations with both their Super Rugby enviroments and also the All Black coaching group.
"They all know we love them to death and we'd love them to stay, but they've got to make their decisions."
Tew said NZR was getting closer to signing All Blacks captain Kieran Read, who was also off contract next year, through to the end of the 2019 World Cup.