South Korea failed to top their group and although that saw them avoid Japan in the first round of the knockout stage, it put them on a collision course with three-time champions Saudi Arabia who finished first in their group.
Saudi Arabia have also had the upper hand in the Asian Cup having never lost to South Korea in three encounters but Klinsmann predicted a "nail-biter" and said the match could even go to penalties.
"I don't fear anybody. No fear but a lot of respect for every opponent," Klinsmann told reporters ahead of Tuesday's clash where the Saudi supporters are expected to outnumber the South Koreans at Education City Stadium.
"Roberto is doing a fantastic job, it's a step-by-step process that he had to go through. It's obviously a new adventure for him and a new adventure for me being in Korea.
"We have a lot of respect for Saudi Arabia. I've played Mancini many times in my career... You can now see his handwriting on the team after 10 games."
Klinsmann was seen smiling in the dugout when South Korea conceded an equaliser against Malaysia in the 15th minute of stoppage time, with critics saying it was part of the plan to avoid topping the group and facing Japan, Asia's top-ranked side.
But the German said their aim was to top the group and that his smile had nothing to do with who they faced in the knockout phase.
"My smile was because I saw it coming. It was a game where we had nearly 85% possession, 20 corner kicks, many chances and did not score another goal," he explained.
"Usually in football, this is what happens in the very last minute if you don't finish off the game, you get punished."
Mancini's side lost to South Korea in a friendly match last year soon after he took over the team and the Italian is not taking Klinsmann's side lightly even though they conceded in all three group games.
"South Korea is a very good team. Just because they conceded six goals in the group stage doesn't change their strengths," Mancini said.
"We play one of the best teams in the tournament. Not just their attackers, the whole team is good. They have speed and quality with players who play in Europe.
"But we've improved a lot in the past month and we're positive."
