Eight points clear with four games left, Dortmund will win their first championship since 2002 if they win at Borussia Moenchengladbach on Saturday and second-placed Bayer Leverkusen fail to beat Hoffenheim.
While Dortmund are trying to focus on the game and keeping title talk to a minimum, some 19,000 travelling fans will make the trip for the match, the largest number since their 1989 and 2008 German Cup finals, the club said.
Training sessions on Thursday and Friday were closed to fans as coach Jurgen Klopp tried to shield his players from the growing waves of spectators.
"I hope our fans understand the need for this measure," Klopp said. "At the end of the day it is in our interest to prepare in a professional manner for the game in Gladbach."
Klopp will be without key playmaker Nuri Sahin, who partially tore ligaments last week and will miss the rest of the season.
This is unlikely to spoil their offensive appetite against last-placed Gladbach, who have their backs to the wall and in desperate need of a win if they are to have any real hope of staying up.
Third-placed Bayern Munich will be looking to make it two wins out of two games under interim coach Andries Jonker when they travel to Eintracht Frankfurt.
A win would keep them in the running for a third-place finish that would see them play in the Champions League qualification spot, with next season's final to be held in Munich.
Hanover 96, just a point behind in fourth place, travel to Freiburg later on Thursday in a schedule change because of the Easter holidays and a win could lift them provisionally above Bayern.
Champions League semi-finalists Schalke 04, who face Manchester United next week, host Kaiserslautern three days after talismanic goalkeeper Manuel Neuer announced he would not extend his contract beyond 2012 after 20 years with the club, making a move in the summer all but inevitable.
Neuer, 25, said he expected some jeers and whistles from the same fans he sat with in the stands as a teenager.
