Dortmund, better than championship leaders Bayern since the winter break, are in second place on 64 points, with the Bavarians, on 69, chasing a record fourth consecutive Bundesliga title and a treble.
Dortmund could also potentially end up with three titles, if Bayern slip up, with the team still involved in both the Europa League and German Cup.
Tuchel had stated that his pre-season goal was not so much as claiming a league title for the first time since 2012 but delivering a campaign worthy of the club's name, especially after last season's travails.
They were bottom at the halfway stage in the 2014-15 season and despite a late surge, missed out on Champions League action as Klopp announced his intention to depart in April.
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This season, however, they have shadowed Bayern since the start of the campaign and have built up a 16-point lead over third-placed Hertha Berlin with Schalke 04 a further four points adrift in fourth.
Victory against Bremen would secure a top-three finish or even a top-two spot if Hertha lose at Borussia Moenchengladbach, guaranteeing a return to Europe's premier club competition.
Tuchel has midfielders Julian Weigl, who recovered from a throat infection this week, and Sven Bender available, though the participation of Ilkay Guendogan remains in doubt.
The Germany international, nursing a foot injury for the past few weeks, has yet to return to full training with the team and poorly central defender Neven Subotic is also doubtful.
Werder, a point above the relegation zone, could be without Peru striker Claudio Pizarro, who picked up a back injury in a 1-0 World Cup loss at Uruguay on Wednesday.
"I pulled my back towards the end of the first half," Pizarro, who will undergo medical checks later on Thursday, said. "After the break, I tried to play on but I could not do it without it being painful."
Bayern, who take on Benfica in the Champions League quarter-finals on Tuesday, host Eintracht Frankfurt, who will set a new league record if they fail to score against the league leaders for an eighth consecutive encounter with the Bavarians.
(Reporting by Karolos Grohmann)
