Dubbed 'Neverkusen' for their failure to win anything over the past three decades, the team have come close to league success on several occasions and also reached the Champions League final in 2002.
However, they last won silverware in 1993 with their German Cup triumph.
Leverkusen have yet to lose in any of their three competitions this season, with the Germans through to the Europa League quarter-finals where they face West Ham United, and in the German Cup final.
"I don't know if I can even describe the feeling," Leverkusen's Robert Andrich told broadcaster RTL.
"I will probably collapse. But when I lift the trophy aloft, by then it will have sunk in a bit more."
Even if Leverkusen secure the title on Sunday they will not get their hands on the trophy until the final matchday.
Bayern, after back-to-back defeats by Borussia Dortmund and Heidenheim, are desperate to bounce back and secure second place though they have VfB Stuttgart breathing down their necks in third, with both teams on 60 points.
The Bavarians got a shot of confidence with Tuesday's 2-2 draw at Arsenal in their Champions League quarter-final first leg but Thomas Tuchel's team have been far from their best domestically.
Tuchel is leaving at the end of the season, a year before his contract is up, and while Bayern bosses have said he would see the campaign out another loss on Saturday could complicate matters, especially ahead of Wednesday's return leg against Arsenal.
Stuttgart host Eintracht Frankfurt on Saturday while RB Leipzig, fourth on 53 points, take on VfL Wolfsburg.
Fifth-placed Borussia Dortmund, also on 53 points and battling for a Champions League spot next season, travel to Borussia Moenchengladbach.