"We would like him to assert himself physically in the game because it's an element which you can't avoid at Test level.
"He's got a great opportunity to do that and hopefully dent the Lions' belief at the same time playing for the Reds."
McKenzie, though, says it's unfair for Deans to only now place such demands on Cooper, who is seemingly still paying the price for criticising the Wallabies' culture last year in an outburst that led to a $60,000 fine and three-match ban for the midfield star.
"Myself, Robbie and Quade had a discussion about Quade and where he defends at the start of last year and we haven't had any discussions since," McKenzie told AAP from South Africa.
"So now he has one match to defend in the front line to make the Lions squad? It's easy to say that now. What's he been saying for the last 13 weeks?
"It's not like he hasn't been defending in the front line anyway. He defended there last night (against the Cheetahs) and he defended there against the Hurricanes.
"We've used him in different defensive systems throughout the season."
McKenzie noted that Queensland won the Super Rugby title in 2011 with Cooper defending at fullback and were unable to retain the title after moving Cooper into the front line last year.
"We also want to make an investment in counter attack (with Cooper playing fullback)," he said.
"So we went back to our old system this year and look what's happened - we're at the pointy end of the competition."
McKenzie also questioned O'Connor's defensive starch.
"Is James O'Connor in the squad? What happens when they run over him? He got speed-humped the other day. What was that?"
Cooper, who McKenzie claimed was "tackling at 70 per cent in the front line" for the Reds this season, could yet force his way into the squad.
"People will say that's the end for Quade, but that's not the case. There's still six positions to be resolved," Deans said.
"We all know Quade's history in the group. I've selected him on 38 occasions, I understand. So he's had a lot of faith and support from me. To suggest otherwise is nonsense."
No sooner had Deans overlooked Cooper was two-time World Cup-winning Wallaby Tim Horan tweeting that the Brisbane Broncos were circling the 25-year-old in the hope of luring him to the NRL.
- AAP