In announcing his 20-man squad on Wednesday, Meninga said he would like to see Thurston pull on the green and gold jumper if he was passed fit but emphasised he didn't have to play this weekend to be cleared.
Meninga naturally wants to run out his best 17 against the Kiwis with a World Cup at the end of the year, however he has James Maloney waiting in the wings as cover.
The Cowboys are understandably nervous about pushing Thurston too far too soon given fullback Lachlan Coote's ongoing problems with the same injury and the champion playmaker's importance to the team after co-captain Matt Scott was ruled out for the year.
"If it was a final or a big game, we'd consider taking a risk but it's always a calculated risk," Green said.
"At this stage of the season there's no reason to risk him being out there."
It also puts the Cowboys' medical staff in a difficult position given they also serve on the Australian team.
Asked about the potential for him to butt heads with Meninga, Green said: "I'm sure (Meninga) does want him to play, everyone wants him to play.
"But that's a decision we'll talk about if he doesn't play on the weekend."
- AAP
