The Germany international missed Bayern's matches against Arsenal, Freiburg and Magdeburg but has now returned to the training ground and is hoping to be available for the meeting at the Allianz Arena.
Assistant coach Aaron Danks, who is standing in for Vincent Kompany, confirmed that Kimmich had so far trained individually but was scheduled to join the full squad for Friday's final session.
Sporting director Max Eberl stressed that Bayern would give the midfielder all the time and support he needed during a difficult period.
"Life is different for him now and we don't need to hide that," Eberl said.
"We will give him all our support. When Jo feels ready to immerse himself in his new daily routine, the coaching staff will discuss with him whether tomorrow is the right time for him."
While Kimmich could be available, Bayern will again be without goalkeeper Manuel Neuer.
The experienced shot-stopper has been sidelined with a foot problem since the 2-2 draw against Arsenal in the Champions League and is not expected to return against Dortmund.
Jonas Urbig will therefore continue deputising between the posts, with Danks confirming that Neuer's condition will be assessed daily.
"We will monitor him day by day until next week," Danks said.
Bayern host Dortmund at the Allianz Arena on Saturday in a major Bundesliga showdown.
Dominic Calvert-Lewin has expressed his eagerness to partner Harry Kane in England's attack, insisting he would welcome the chance to demonstrate how effectively the pair could operate together.
Bayern Munich have confirmed that Manuel Neuer has suffered a partial tendon tear in his right foot, raising further concerns over the veteran goalkeeper's fitness.
Bayern Munich honorary president Uli Hoeness has admitted that Jamal Musiala may never return to his previous level of performance because of an underlying neurological condition.
Schalke head coach Miron Muslic took encouragement from his side's performance despite suffering a 2-1 defeat against TSG Hoffenheim in the Bundesliga.
