Leipzig host Bayern on Saturday evening, just hours after fellow Champions League participants Borussia Dortmund and Bayer Leverkusen do battle in Dortmund.
The two games are expected to set the tone for what many are predicting will be a three or four horse title race.
Germany great Lothar Matthaeus claimed last week that Leipzig, who finished third last year and reached the German Cup final, were definite title contenders under new coach Nagelsmann.
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"I am always happy when experts like Matthaeus see the team's development positively -- now we have to confirm it." said Nagelsmann on Thursday.
"The game will not be decisive for the title race, but a win can give us a lot of confidence," he said.
The 32-year-old coaching prodigy said that in-form striker Timo Werner could make the difference against Bayern.
Werner, 23, has scored five goals in three games already this season.
"He is on a good run, and he can really hurt Bayern," warned Nagelsmann.
Bayern are still without Leon Goretzka after the midfielder underwent a thigh operation this week, but they otherwise return from the international break at full strength.
The champions, who trail Leipzig by two points in second place due to their opening day draw with Hertha Berlin, can go top with a win on Saturday.
"This is where the season gets going," said coach Niko Kovac on Thursday.
"We have six games until the next break, and we want to position ourselves high in the table."
"The game against Leipzig is important in that regard."
Yet Kovac also insisted that Leipzig were not Bayern's only contenders for the Bundesliga title this season.
"You also have to mention Borussia Dortmund and Bayer Leverkusen," he said.
"Those were the top four teams last year, and I think they will share the spoils this year as well."
Yet Dortmund, who sit one spot behind Leverkusen in fifth, are under growing pressure after a recent dip in form.
Coach Lucien Favre has faced criticism in the German media following a shock 3-1 defeat away to promoted side Union Berlin at the end of August.
Bild newspaper claimed Wednesday that some players were disgruntled with Favre's selection and tactics, calling the atmosphere around the club a "powder keg".
On Thursday, Favre insisted that he still had the support of the dressing room.
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"We have lost one game. The trust is still there. We need to look forward and be positive," said the Swiss.
"We know about Leverkusen's quality. It is no coincidence that they finished fourth last year," he added.
Saturday's game will see Leverkusen coach Peter Bosz return to Dortmund for the second time since his ill-fated, six-month spell in charge of the club in 2017.
The Dutchman's reign at Dortmund ended in disaster after a nine-game winless run, but he has since restored his reputation by leading Leverkusen into the Champions League last season.
Leverkusen midfielder Sven Bender, a former Dortmund player himself, said this week that Bosz was a "sensational coach".
Dortmund midfielder Julian Brandt will also come up against his former colleagues on Saturday, having left Leverkusen for 25.5 million euros ($28.1m) in June.
With Belgian winger Thorgan Hazard still out injured, Brandt is expected to start against his old club.
Elsewhere this weekend, Cologne host local rivals Borussia Moenchengladbach in the Rhine derby on Saturday, while David Wagner's Schalke travel to promoted side Paderborn on Sunday.
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