Klopp put pen to paper on a two-year contract extension on Wednesday, announcing the new deal at a press conference scheduled to talk about his side's upcoming clash with the Swabians.
Inevitably, the discussion followed a different path for much of the allotted time, although Klopp did find the time to confirm he had been analysing his side's next opponents parallel to his contract negotiations.
"There are a lot of things we've got to watch out for," Klopp said.
"Stuttgart have a lot of quality and they're in good form. As soon as they gain possession, you've got to be right there.
"It would be good if we could present ourselves in this home game in the way we should do, the way the fans recognise us, with all our extraordinarily positive facets."
Stuttgart coach Thomas Schneider does not need reminding of what those positive facets are, but he has no reason to doubt the ability of his own team either.
With three wins and four draws since he took charge, Stuttgart have climbed from the foot of the table to eighth, and they could move to fourth with a win.
"We're really looking forward to it," Schneider said at a press conference.
"The lads know what to expect and they're excited.
"It's an absolute highlight to play against one of the top teams in Europe, and Friday night games are always special."
Schneider will assess the fitness of Daniel Schwaab, who took a knock to the ankle against Nurnberg, before deciding whether changes will be made to his side.
With one eye on the Champions League clash with Arsenal on Tuesday, Klopp may make alterations to his usual starting XI.