That number may change with injuries in the Air New Zealand Cup, with Doug Howlett now a doubt after a knee injury in Auckland's quarter-final win over Bay of Plenty.
But Henry, who confirmed last month that a third hooker and half-back would travel to Britain and France, said there was still room for players to impress.
He told the Dominion Post: "There are four positions in the 32 where we are looking at alternatives. We've got our favourite and one or two others we are looking at.
"This tour will be more difficult because we play two Tests against France, who are the number two ranked side in the world, and Tests against England and Wales, and we've got a six-day turnaround between England and France."
The former Wales boss accepted his first-choice squad was at the mercy of the elongated domestic season.
"It was always on the cards when you have guys playing in a knockout competition," he said.
"It was the same last year and we will just have to modify our training so the guys who need extra contact and physical training get it, and those that don't, don't."
Howlett remains unlikely to tour and utility back Luke McAlister is also a doubt with an injured shoulder.
Forwards Ali Williams (neck) and Richie McCaw (concussion) will be considered, although another moment of blurred vision for the skipper may not bode well.
Henry will name his All Blacks squad following the Air New Zealand Cup final later this month.