Liverpool, under the tutelage of Rafael Benitez, famously came back from 3-0 down to win on penalties against AC Milan, in the 2005 Champions League final.
Ahead of the Super Cup clash against Chelsea, Klopp is hoping to write another chapter of the club's history in the Turkish city.
"I know how special Istanbul is for every Liverpool supporter," he said at his pre-match press conference.
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"Nobody will forget 2005, but we are different people, we aren't the same – we are the 2019/20 team, a very good one too!
"Istanbul is a great place for football, I played here once with Dortmund and the atmosphere was brilliant. There's a big community of Liverpool supporters here in Turkey and that makes it special for us too.
"We are fresh, we want to play and hopefully we can make it a special place for this group too."
Klopp was also keen to play down his side's status as favourites against Chelsea, despite Frank Lampard's team's 4-0 drubbing at Manchester United in their Premier League opener on Sunday.
"I didn't know everyone expects us to win! That's not a problem.
"We respect them a lot, we saw their game against Man. Utd, and the result was deceiving.
"They made changes, new manager, lost Hazard, lots of new boys, Christian Pulisic, brought in all the young boys like Tammy Abraham and Mason Mount, a good team with a really interesting plan.
"Frank did an outstanding job at Derby last season. He changed the football there, to make them a football-playing side.
"It was not easy but he did it and they were a storng side and unlucky not to get promoted against Aston Villa.
"But now they are fresh, everyone is on their toes and it is the first time they have been together.
"They will be 100 per cent ready so we have to make sure we are as well. Everything that doesn't affect us, we have to ignore and that's what we do actually."
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