New Zealander Deans is contracted until after the World Cup but Campese believes he should then be replaced by a victorious McKenzie, despite the Australian Rugby Union appearing keen to retain Deans' services.
"If the Reds win, Ewen McKenzie should become the Wallabies coach," Campese told AAP.
"I know they want Robbie Deans signed but we don't need him.
"I would rather Australia have an Australian coach than sign Robbie Deans again.
"McKenzie has taken the Reds from almost last to first so he's definitely got the players playing well and he deserves to be the national coach."
McKenzie's stats with the Reds are certainly impressive. The former Waratahs coach boasts a win record of 70 per cent since joining from Stade Francais in 2009.
The 51-year-old has taken the Reds from second bottom to top of the Super Rugby pile in two seasons and is now hoping to secure the franchise's first-ever Super title with victory over the competition's most successful side this weekend.
McKenzie was offered the Wallaby job in 2005 but turned down the chance to replace Eddie Jones in the hot seat, opting instead to stick with the Waratahs.
Campese's comments are perhaps unsurprising given his objection to Deans' original appointment and the fact that he played alongside former prop forward McKenzie during the Wallabies' 1991 World Cup triumph.
But they are unlikely to have any effect on the ARU who are keen to get Deans to commit to a contract extension before the World Cup starts in early September.