McKenzie has been struggling with an ankle problem that kept him out of the 50-19 victory over the Bulls in Pretoria on Saturday, but there is better news around wing Will Jordan (back) and scrumhalf Cam Roigard (calf), neither of whom have played for a month.
"Both Will and Cam got through a bit of training, we are pretty confident they're going to be right for next week. Both of them we want to have a full week of training, but they're certainly ticking enough boxes," Rennie told reporters after the Bulls game.
"We are probably less confident about Damian, but still think he has a good chance to play. Hopefully he can train well on Tuesday."
There are several other bumps and bruises from the victory over the Bulls, the All Blacks’ third on their Rugby’s Greatest Rivalry tour of South Africa.
Prop Xavier Numia has a stiff Achilles and scrumhalf Cortez Ratima took a blow to the knee.
The All Blacks are embarking upon their first full tour of South Africa since 1996! Marketed as the 'Greatest Rivalry' series, the winner will come out not only with the bragging rights but World Rugby's number one ranking. Keep up to date throughout August and September with news, previews and more.
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Rennie was pleased with a victory that has provided food for thought over team selection for the first test, though facing the Springboks will be a few levels up from their games on tour so far against depleted provincial sides still in their pre-season.
"There was a lot of good performances, I thought Pete Lakai was excellent until we took him off, Anton (Segner) was massive. Those guys are applying a lot of pressure (to start against South Africa)," he said.
"That certainly wasn't our test side, so there will be a number of changes, but there was some really good performances that will put pressure on us from a selection point of view.
"What we know is that the intensity level and the quality that we are going to come up against next week is three, four, five-fold. But we've played reasonably well on tour and we know we need to up the ante.
