The same weekend, NSW play the Western Force in Perth while Queensland, who have a Super bye, host the Lions at Suncorp Stadium.
Still tormented by missing last season's finals by one point following a last-round upset loss to the Blues, White said every competition point would be hugely important to his team's play-off hopes that late in the competition.
"Last year in the last round our whole season changed so I find it highly unlikely that in the last rounds this year that the expectations from anybody would not be to play your best teams," he said.
"We're all happy to help [the Wallabies] but it's making sure everyone wins. We can't have this situation."
McKenzie has said he'd be prepared to compromise by allowing test players to start their camp on June 2 in the hope they'd be released towards the end of the week to play that weekend.
But that would not appease 2007 World Cup winner White who feels he needs his young, improving side together for a full week to prepare for their clash with the Rebels.
"Ewen is in a different situation because he's talking about a Lions [tour] game and he also has a very settled team.
"It makes no difference if one guy [Quade Cooper] boxes one Saturday and plays the next Saturday - there's not many teams who can afford that," White said.
"The Waratahs have a Wallaby pack of forwards who play together every Saturday - if it's not for the Waratahs it's for the Wallabies.
"We're in a very different situation.
"We can't afford to lose four guys or five guys and then by Saturday they're back to play."
The Brumbies provided eight of 49 players to a Wallabies logistics camp this month and they have no issue with resting test players from their Lions tour clash on June 18.
White confirmed Pocock would make his Brumbies debut tomorrow night against his old Force teammates in a Darwin trial.
Former Wallabies winger Clyde Rathbone will also make his comeback, playing at centre outside playmakers Matt Toomua and Christian Lealiifano who will trial at 10 and 12 with McCabe (neck) sidelined until round four.
- AAP