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The former Reds forward was placed in interim charge of the Turkish outfit last week having joined the staff as assistant during the summer.
The sides meet in Istanbul for matchday four of the Champions League, bringing together two clubs Kuyt holds dear.
The Dutchman made 285 appearances and scored 71 times in a spell at Anfield from 2006 to 2012, then had three years with Fenerbahce as a player and won the league there.
“First of all, it was a really special achievement to reach the Champions League for the first time in 18 years for Fenerbahce,” said Kuyt at his pre-match press conference today.
“That was something really exciting and at the moment you reach that stage you know you’re going to play against very exciting teams.
“As soon as the draw came up, as a technical member of the staff I was really excited because everyone knows how much Fenerbahce and Liverpool mean to me.
“From that moment, you know it’s going be a special occasion.
“Of course tomorrow will be a very, very special occasion for me. But at the stage we are in, I’m not the important person. It’s the club.
“Romelu [Lukaku] was speaking about how important it is to show the fans – who deserve much more – a reaction of positive energy and a good performance.
“We have really good players but we need to show up. When we show up tomorrow with good energy, with passion and there to play, I think it can be a very special night.
“Liverpool are an amazing team but so are Fenerbahce. If the fans will show up, I think Europe will see how big this fan base is.”
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'We are Liverpool' podcast - Dirk Kuyt looks back on his Reds career
Kuyt continued: “It’s a big opportunity for Fenerbahce. It’s a big opportunity for the players; in the first place, they need to show.
“We have a good plan for tomorrow but we need to believe in that plan. And I believe the players are believing.
“If we show that with passion and energy then my biggest wish is that the fans of Fenerbahce are showing themselves to Europe on the highest stage, a big platform, Champions League, against one of the biggest teams in the Champions League.
“This is very special and that’s why I’m looking so forward to it.
“From the first moment the players enter the pitch, I’m 100 per cent convinced the fans will be behind us.
“That will be our biggest power. I think that will be our biggest chance to have a good performance and hopefully a good result.”