Bayern currently lead the Bundesliga with 38 points from 15 games, scoring 41 goals and conceding just six.
Augsburg, meanwhile, did manage to lift themselves off the bottom of the table last weekend, but they still have 30 points less than their guests and have scored just 11 times.
"Nobody gives us a chance of getting anything against Bayern, but that's precisely what we want to do," said Weinzierl.
"We want to win the game. In the cup, a third-division team can beat a Bundesliga side, and Nurnberg got a point against Bayern a few weeks ago, so why shouldn't we be successful?"
Despite the odds being stacked against Augsburg, Weinzierl has been encouraged by his side's recent performances, even if the results have not quite reflected this.
He is therefore planning to get at Bayern and not just be negative at the Augsburg Arena.
"We want to play well and impose ourselves on the game," he said at a press conference. "If Bayern are constantly in or around our penalty area, then it's tough to get anything, which is why we have to keep them away from our goal and have faith in ourselves.
"With our unity, we can survive against the dominant league leaders and top favourites.
"One thing I can promise is that we will give everything to get a successful result."
The two sides will meet again in 10 days' time in the DFB-Pokal and, until then, Bayern will not be allowed to give an inch by their coach Jupp Heynckes.
"The whole team is hungry for success," he said. "We are going to keep it up right through to the cup game."
Heynckes is likely to be without Claudio Pizarro due to illness while Arjen Robben is not yet an option either, despite stepping up his comeback from an injury which has kept him out for the past three weeks.
Sebastian Langkamp is Augsburg's biggest doubt, but Tosten Oehrl is available.