The injured Adam Hastings has been replaced by Finn Russell in the Scotland squad.
Hastings has returned to his club Gloucester after being forced off with a head knock and is also having his knee looked at.
Hastings, Kinghorn and Thompson were picked ahead of Russell by the coach.
Finn would be in the running if Adam was out.
Russell pressed his case for a recall when he scored a try and kicked three conversions and a penalty as Racing 92 defeated Perpignan 44-20.
Russell was left out of the initial squad due to questions over his form and consistency.
The former Lions and Scotland fly-half said he had not spoken to Russell since he was not in the original squad.
Kinghorn missed a late penalty that would have given Scotland victory against Australia in the first Autumn series match.
Thompson provided cover on the bench because Hastings was not available for that match because he plays rugby in England.
Kinghorn and Thompson will be vying for the number 10 jersey against the All Blacks.
When the former Glasgow fly-half walked out on the squad before the Six Nations in 2020 he strained his relationship with his coach.
Russell was dropped from the starting line-up for last season's Six Nations finale against Ireland after being one of six players to have an unauthorized night out in Edinburgh.
Wales was crushed 55-23 by New Zealand in Wales, while Scotland lost to Australia by a single point.
Six days after facing the All Blacks at Murrayfield, Scotland plays Argentina, who beat them in a summer series.
Turner scored one of Scotland's four tries on Saturday and is still in the Scotland squad despite an injury.
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