Never say never. Sebastian Kehl and Sven Bender are DMs that Klopp deployed many times in that position. But players like Gundogan and Sahin aren't DMs; they're more DLPMs.
Klopp doesn't impose roles on players, except in the loosest possible sense.
The midfield is expected to be not only dynamic, working as a unit and pressing, but also interchangeable, which is why sometimes you see Henderson starting from deep, and other times, leading the press.
If Lallana tracks behind Henderson (or Wijnaldum), you'll see them push up into his zone and do the job of ball carrier or front presser.
The key to any Klopp midfield, and attack, is fluidity rather than pre-defined roles, with each player expected to know how and when to interchange.
This idea of rigid roles is one that came with Rafa, and Klopp is completely different in his approach.
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