Bayern hammered Bundesliga bottom side Energie Cottbus 4-1 on Saturday and Klinsmann insisted his side began the recovery process immediately with ice baths and long warm-downs to get ready for their Group F clash.
With two wins and two draws, Bayern are level with leaders Lyon and a win over bottom-of-the-group Steaua at Munich's Allianz Arena will guarantee their place in the next round.
"We have a big chance to advance into the round of the last sixteen in the Champions League," said Klinsmann.
"So from now until kick-off, the entire concentration in everything we do has to revolve around Steaua Bucharest."
And Germany midfielder Bastian Schweinsteiger said the players are just as keen to get the win they need on Tuesday.
"We want to decide the situation ourselves and make our place in the last round secure," said Schweinsteiger.
Bayern expect to welcome back Germany star Lukas Podolski after the striker missed the victory over Cottbus with a bruised thigh having picked up the injury as a second-half replacement in the 2-1 defeat against England last Wednesday.
And Argentina defender Martin Demichelis, who scored the first goal against Cottbus, was substituted at half-time by Klinsmann as a precautionary measure.
Steaua Bucharest come to Munich with no hope of advancing into the next round.
All that is left for them in their third successive Champions League outing is to secure a third place finish in the group that would be enough to ensure a UEFA Cup qualifying berth.
Bucharest are fourth in the Romanian league and drew 0-0 with third-placed Universitatea Craiova on Friday.
History is against the Romanians under coach Dorinel Munteanu - their six previous trips to Germany for European competitive fixtures have not yielded a single victory.
Their best result was a 0-0 draw in Munich against Bayern in 1972.
And although Munich trail Lyon on goals scored in Group F, the German giants are in a comfortable position that only the twin occurrence of Bayern losing at home and Fiorentina beating Lyon will stop the German team celebrating reaching the next round.