Third-placed Frankfurt are level on 20 points with Schalke, seven behind Bayern, who have won nine of their 10 league games in a scintillating run so far.
Eintracht coach Armin Veh, no stranger to the big time after steering Stuttgart to the 2007 Bundesliga title, said his players knew what they were up against but were entitled to think big.
"It is important to allow dreams," Veh told Bild newspaper. "It is also possible to achieve things with less money. There are times you have to believe in yourself."
Veh guided Eintracht back into the top flight after a season in the second division and has since seen his team win six games, draw two and lose two to remain behind Bayern and well ahead of champions Borussia Dortmund.
Their attacking style has been a hit among fans this season, with Alexander Meier already scoring seven goals, and Frankfurt have the best offence after Bayern in the Bundesliga.
Veh warned, however, that their league rivals had now got used to their attacking game.
"Teams will be more physical now and we have to adapt to that but I do not want to change our style one bit."
The Bavarians, without a domestic or European title in two seasons, are eager to put more distance between themselves and their rivals as they look to solidify a big lead going into the winter break in December.
The Bavarians have a multi-million-euro squad that does not compare to Frankfurt's much cheaper line-up.
"(Bayern's Javi) Martinez cost 40 million euros to buy and probably gets 10 million euros a year," said Veh.
"With the 50 million of just one Bayern player we could finance our entire team for two seasons, so the chances are not really equal."
The Bavarians are also brimming with confidence following their 6-1 demolition of France's Lille in the Champions League on Wednesday and a 3-0 win at Hamburg last week.
Bayern CEO Karl-Heinz Rummenigge, however, warned that Frankfurt were dangerous.
"They should have respect for us but we also have respect for Frankfurt," he said. "They are playing a great season and we will have to do everything possible to maintain this wonderful lead we have."
Fellow Champions League competitors Schalke host improving Werder Bremen while Dortmund, in fifth on 16, take on bottom-placed Augsburg.