McKenzie, as well as fellow All Blacks Anton Lienert-Brown, still owed on All Blacks stand-down week in Super Rugby, but as their campaign gets back underway against the Highlanders in Fiji this weekend, the pair will both be lining up.
The Chiefs will also welcome back Tyler Ardron and Sam Cane after stints on the sidelines due to injuries.
The Hamilton-based club have three games left to play, with the Highlanders this week before back-to-back home games against the Brumbies and Hurricanes before the playoffs.
"We're very confident," Cooper said of his side heading into the business end of the season. "We believe we're going to be there (in the final) on August 4. Our whole focus is about week by week to make sure we're there.
"It's more concentrating on what we're going to bring than what the opposition's going to bring."
While a number of players return to the side this week, lock Brodie Retallick remains out with a pectoral injury, while Nathan Harris has been allowed to remain in New Zealand with his partner and their newborn child – provided his teammates stay healthy.
"I said to Nathan, if we do get a sickness in Fiji you're going to have to come."