The former Liverpool target prefers current Dortmund coach Thomas Tuchel.
Klopp, who left the German club last summer, brought the 27-year-old to Dortmund in 2013 - a transfer which reportedly saw the Armenian playmaker reject the chance to join Brendan Rodgers's Liverpool side (The Mirror).
The duo will be reunited next month when the Reds square off with the Bundesliga giants in a two-legged Europa League quarter-final, the first of which comes on April 7 at Signal Iduna Park.
Mkhitaryan is one of several players appearing to thrive under coach Thomas Tuchel, having netted 10 league goals - more than he did during any of his two seasons with "football madman" Klopp.
“With Klopp, he was a football madman: pressure and counter-attack,” he told Gazzetta dello Sport, via the Liverpool Echo. “Instead, Tuchel has changed our lives.
"Now we command the game and I have more freedom to attack. Thanks to him I now make myself more useful.”
Klopp, 48, won two Bundesliga titles during his successful eight-year spell at the club, and also guided them to a Champions League final in 2013, before being beaten by Bayern Munich.
Consequently, the manager is likely to receive a rousing reception from the Dortmund fans in both legs of the last-eight tie.