Kompany was discharged from hospital on Wednesday after collapsing during a training session last week because of meningeal irritation. The Belgian is expected to remain away from the team for some time as he recovers.
Danks took charge of Bayern for their German Cup victory over Magdeburg and will again lead the team against Dortmund at the Allianz Arena.
"We want the players to go out and show who they are," Danks said on Friday.
"No big changes, no big differences for us. We will be ready and super competitive."
The English coach acknowledged that his approach would naturally differ from Kompany's, but stressed that the coaching staff worked well together.
"There is a difference. Vinnie did not want his assistant coaches to be mini-Vinnies. We are all different, but we complement each other," he explained.
Bayern and Dortmund are level on points at the top of the Bundesliga, with the Munich side leading only on goal difference. Saturday's Klassiker is therefore a major test in the battle for the title.
Bayern board member for sport Max Eberl said the club had been able to manage Kompany's absence through the strength of its coaching team.
"What happened with Vinnie is difficult to prepare for," Eberl said.
"What we said at the start of his illness is that we have a coaching staff. Vinnie is up front with a big personality, but there is a whole team."
He added: "It is nothing new for the lads. It is not a situation we could have planned for, but we have seamlessly made the transition."
Danks is expected to remain in charge for Bayern's next few matches, including Tuesday's Champions League trip to Atletico Madrid, as Kompany continues his recovery.
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.
