The opening match in Sydney on Saturday has been eagerly awaited in Australia since McKenzie was installed as head coach after Robbie Deans fell on his sword following his team's 2-1 series loss to the British and Irish Lions last month.
New Zealander Deans had refused to select Cooper for the Lions series after a falling-out last year when the enigmatic Queensland Reds playmaker described the Wallabies environment as 'toxic' and restrictive for his natural game.
McKenzie, however, had publicly backed Cooper throughout and given him license to play his helter-skelter style while at the Reds.
McKenzie had refused to discuss his team composition and media reports across the Tasman suggested he will select the uncapped Toomua, who helped the ACT Brumbies to the Super Rugby final and is more of a steadying influence in the Canberra-based side's conservative game plan.
"I actually think the better question is, 'is he feeling ... challenged' because he doesn't know which five-eighth (fly-half) he wants to play," Hansen said when asked if he felt under pressure with McKenzie's mind games.
"He's in a difficult situation because I'm imagining when Robbie Deans wasn't picking Quade Cooper, he was saying 'I'll pick you Quade, I'll pick you'.
"Our information is telling us that he's going to pick the other bloke."
Hansen said he felt that McKenzie was worried about the pressure of expectation that would be placed on either Toomua or Cooper, who has not played well against the All Blacks in the past and was anonymous in the Reds' Super rugby playoffs loss to the Crusaders last month.
"There's only one or two reasons why he doesn't want to tell them," Hansen said of McKenzie's refusal to discuss his potential side.
"He's not sure for himself or he doesn't think they can cope with the pressure of being in the public too early. So it's not effecting us, it doesn't bother me who they play.
"I think they will pick Matt (Toomua) and possibly also pick both midfielders from the Brumbies (Christian Leali'ifano and Tevita Kuridrani) and use their defensive screens and their rush defence to put us under pressure that way."
While McKenzie had been feted in Australia as the man to turn the Wallabies' fortunes around after they won just three of the 18 tests against the All Blacks under Deans, Hansen said he would still be under pressure on Saturday.
"I only have to think back to my first test match as head coach and whether you want to admit it or not, there is pressure," Hansen said.
"Australia haven't had a great run against us for a wee while now and that's been attributed to Robbie Deans, which I think is a bit unfair.
"And everyone seems to think that Ewen is going to make the difference so there has to be pressure on him. Well what happens if it doesn't work? There is a lot of pressure there.
"That's why they will turn up and give it everything they have got, so we have to match that intensity or better it."