Klopp, who has held an advisory position across Red Bull's football network, is taking charge of the German national team, but Leipzig chief executive Tatjana Haenni believes the impact on the club will be limited.
"Jürgen Klopp was a kind of advisor for us," Haenni told Bild.
"The fact that there is now going to be a change only affects us indirectly here at RB Leipzig. We want to continue working in exactly the same way – with or without Jürgen Klopp.
"Of course, you're always happy when you have expertise around you. I also believe you're simply better when you have expertise at different levels. But we don't feel like we immediately need to find someone new tomorrow."
Klopp's departure comes at an interesting time for RB Leipzig, with Martín Demichelis only recently beginning work as the club's new head coach. Reports in Germany have suggested Klopp played a leading role in bringing the Argentine to the club, despite some decision-makers reportedly favouring a different direction.
Haenni, however, insisted unexpected developments are part of modern football and said the club is prepared to adapt whenever circumstances change.
"The dynamics are simply part of this business. We're not really surprised by that.
"Sometimes unexpected things happen very suddenly. You're always prepared for something like that because you know it can happen."
Leipzig have undergone significant changes this summer following a disappointing campaign, with Demichelis tasked with leading the club back into contention at the top end of the Bundesliga.
Although Klopp's experience and influence have been welcomed during his time within the Red Bull football structure, Haenni stressed Leipzig's sporting strategy is not dependent on one individual.
Instead, she believes the systems already in place will ensure continuity as the club enters a new chapter under Demichelis.
Leipzig are continuing preparations for the new season with no plans to alter their sporting direction, despite the expected change behind the scenes at Red Bull.