According to Sky, Klopp has told Undav directly that he will not be included, though the decision is currently understood to be only a leaning rather than final. The 30-year-old has struggled for form in the opening weeks of the new season, failing to convert several presentable chances and remaining without a goal for VfB Stuttgart, though he has still managed four assists in five matches.
What the omission means for Undav's longer-term international future remains to be seen, but there is little dispute that his direct, physical style of play does not naturally suit the kind of football Klopp has favoured throughout his coaching career.
The VfB Stuttgart captain has been one of the more popular figures in the national team set-up in recent seasons, making his potential absence all the more notable.
Undav has scored nine goals in 13 caps for Germany, including three at this year's World Cup, all of them coming off the bench. His statistical record at international level stands in stark contrast to his likely omission, underlining that Klopp's selection appears to be based on tactical fit rather than pure output.
Klopp is set to name his first squad on Thursday ahead of Germany's Nations League fixtures, with the new head coach expected to bring in several uncapped players as he begins to reshape the national team following a disappointing World Cup campaign. Whether Undav's absence proves temporary or marks a longer-term shift away from the squad will become clearer as Klopp's tenure progresses.
Germany open their Nations League campaign away to the Netherlands on September 24, before hosting Greece three days later, followed by fixtures against Serbia and a return trip to Greece early next month.
Klopp's early selections will be watched closely for signs of the identity he wants to build heading toward the next major tournament, with his willingness to leave out an established international scorer like Undav suggesting he is prepared to make bold calls from the outset of his tenure.