A 0-0 draw with Mainz last April was the last time Bayern failed to find the back of the net in a league fixture, and although they are now 11 points clear at the top of the Bundesliga, Schweinsteiger says there can be no sitting back.
"We are trying to do one or two things that bit better," he said.
"The decisive pass has got to be more precise so that we can create even greater goalscoring opportunities.
"There are moments in our game when we could position ourselves better and quicker."
Mainz coach Thomas Tuchel is bullish ahead of the match. He has already got the measure of Bayern twice since taking charge and therefore knows what it takes to trouble them.
However, he also knows that even the best is not always good enough against Bayern.
"We have proven often enough that we can exceed ourselves," he said.
"But you can also exceed yourself and get beaten 3-0. If Bayern hit their top form, then our top form is not going to be enough.
"Together with Barcelona, they are the most talented side in Europe."
It does not help that Tuchel is without his most talented player, Adam Szalai, through suspension.
"That is really going to hit us hard, of course," said Tuchel.
"We have alternatives but we won't try to replace Adam like for like."
Midfielder Niki Zimling is in line for his Mainz debut while Bayern coach Jupp Heynckes could name an unchanged side for the third game in a row, again leaving the likes of Arjen Robben and Mario Gomez on the bench.