There are fears that the two sides may play out a stalemate at the Royal Bafokeng Stadium – and dump rivals South Africa and France out of the competition in the process.
FIFA stated last week that they expect all 32 finalists in South Africa to play fairly and Aguirre is adamant that his side will be going all out to win.
“We’re going to try and win,” the El Tri boss said. “We can be first, second, third or even fourth in the group.
“The law of the Mexican side is to win. If as a consequence of what happens on the pitch there’s a draw or a defeat and we both qualify with no major goal differences, then we’ll both be happy.
“But I can guarantee that the Mexican side is going to go out there to try and win.”
The Mexicans, who have a solid record at World Cups, having reached the last 16 in four straight tournaments since 1994, also have the added incentive of avoiding a clash with Argentina in the second round if they can top the group.
Aguirre continued: “My players are very relaxed and know they can be first or second in the group.
“They know they have to be fully focused because we still haven’t achieved anything, so we have no reason to feel happy.
“Mathematically we still don’t have our ticket to the next round and we have to try and take those three points, so that we can achieve our aims for the first round.”
Aguirre’s side have had an excellent tournament so far, drawing the opening match against the hosts 1-1, before easing past France 2-0.
And the coach believes their pre-tournament work is finally paying off.
He added: “We’ve been working together now for about 75 days. Judging by the players’ behaviour on and off the pitch, I think we’re doing very well.
“We’re in good form.”
Two players will definitely be out for Mexico – Arsenal striker Carlos Vela, who has a hamstring problem, and the suspended Efrain Juarez.
Meanwhile, Oscar Tabarez is not worried about who his Uruguay team may play in the next round of the World Cup, despite a potential South American derby against Argentina being on the cards.
A draw in Rustenburg will keep La Celeste in the number one position and help avoid a meeting with their continental neighbours, who are on course to top Group B.
However, Tabarez said: “I’m not even thinking about future matches,” he said. “It’s not a question of wanting to play with this team or that other team.
“I’ve participated in prior World Cups and I know you have to come to a World Cup not thinking about this. We know which rivals we have to play months in advance and all the possible permutations. What we want to do is qualify for the next round and we want to top the group if we can. So I’ve certainly not stopped to think about this.”