Jupp Heynckes' team lead the Bundesliga by 15 points and topped Group F ahead of Valencia to book their place in the knockout stages of the competition they were finalists in last season.
This time, Schweinsteiger claims, Bayern will not accept second best and will not be satisfied with securing a draw in London before the return leg in Munich in March.
| CHAMPIONS LEAGUE LATEST
|11/1||Bayern Munich are 11/1 to beat Arsenal 2-0 with BetVictor
"We say, 'Mia san mia'. Literally it is, 'We are we', but it means, 'We are who we are'. That's not being very arrogant but we are very confident about our ability to win the game. It is about a winning mentality.
"When our players come from somewhere else they sometimes show happiness when the game is 0-0 or 1-1, but we were brought up in an environment where we have to win.
"We are not satisfied with 0-0 or 1-1. This is the mentality of Bayern Munich."
Bayern progressed to the final, which was played at their home Allianz Arena stadium, in 2011-12 but were beaten on penalties by surprise winners Chelsea.
Schweinsteiger missed a spot kick in the shootout that night and, while denying that the pressure of playing at home affected them, admitted that the heartbreak still plays on his mind.
"I still think about that night, of course," he acknowledged. "We didn't feel under pressure because we were at home. We felt very lucky to have the final in Munich.
"We were motivated because it was at home. We felt it was better to be playing at home. It's a pity we were not able to win.
"We were the superior team. It all came down to penalties, just as it did for Chelsea when they lost to Manchester United in Moscow.
"On the night, Chelsea showed 100 per cent of their ability and Bayern did not. With 110 minutes gone I looked up at the scoreboard and thought, 'We have to win the game now', but we could not do it.
"It went to penalties and we lost. Chelsea were lucky and we were not. Maybe it was a good way for Chelsea to make up for losing in Moscow. Maybe it was a matter of fate."
Schweinsteiger believes, however, that Bayern are a stronger side and that Heynckes has more options to choose from this time around.
The Bavarians reinforced their squad by signing the likes of Javi Martinez, Mario Mandzukic, Xherdan Shaqiri and Dante in the summer transfer window.
"We are hungry to win the Champions League," the 28-year-old insisted. "This team have been to the final twice and didn't win.
"We have more experience and we're moving towards our aim. Compared to the final against Chelsea, we are stronger. We have more good players and we are stronger on the bench. This is a crucial point.
"In the final, Chelsea brought on Fernando Torres and Florent Malouda and that helped them win the game. That's a big difference to last season. We have more options to change.
"We are eager to win, we have become a better team and again we are all working towards a return to the final.
"Five or six teams in Europe are candidates to win the Champions League and we are one of them. I know most of Europe do not want to play against Bayern Munich.
"We have gained a lot of respect during the last four or five years, but we have to win against Arsenal before we start to think about this."