A minor hip complaint meant Koch was absent for Saturday's 4-0 victory over Burnley and Bielsa is wary of taking an unnecessary risk with the defender and possibly jeopardising his potential participation with Germany this summer.
Koch - whose first season at Leeds has been disrupted by knee surgery, sidelining him for several months - is therefore not under consideration for Tuesday's trip to Southampton or the visit of West Brom this weekend.
Klich, who opened the scoring at Turf Moor, has no injury concerns but Bielsa insisted he is taking what he feels is the best course of action for the Polish midfielder.
"Koch has been given early leave with the potential for him to be called up or not called up to the German national team," Bielsa said ahead of the visit to take on Saints.
"I don't know whether he's going to be called up to the German national team or not. It's just that he has a small niggle and we didn't want to run the risk of a small niggle being aggravated into something bigger.
"The injury that he has is not important and we didn't want to take the risk of him playing and making it worse so we anticipated his holidays in the same way we did so for Klich.
"(Klich) is not injured. The evaluations that I make over the campaign are for the needs of each player and in the case of Klich, the decision I made was the most favourable one for him."
Bielsa, who revealed Pablo Hernandez could return at St Mary's, saw his side collect their fifth win in their last eight matches, banishing any notion that their approach could result in burnout towards the end of the season.
They are poised for a top-half finish in their first season back in the Premier League ahead of their penultimate game at Southampton, whose results took a downward turn at the start of 2021 after a strong start to the campaign.
"(Southampton) is a team who is in a different position in the table with regards to the performances they have had," Bielsa said.
"They have a group of players who are very capable and they didn't finish higher up in the table because they had a phase of nine or 10 games that was negative.
"But the level of the team is superior to the position they find themselves in the table."
Tuesday's trip to the south coast will be the first time Leeds, as well as Southampton, have played in front of fans in the top-flight for several months and the occasion is not lost on Bielsa.
"England should feel privileged that they are able to partially resolve this situation with Covid and of course it's great to have the fans back," he added. "Even if it's partially, it's a situation that very few countries are able to have."