Kuyt came closest to winning the top flight as a Red during the 2008-09 campaign, when Manchester United pipped Rafael Benitez's team to the title.
But now, as Liverpool currently find themselves eight points clear at the summit, Kuyt is hopeful the current crop of players can go all the way.
The Dutchman told Liverpoolfc.com: "We were very close to success. We just missed a small detail to go one step further.
"With the likes of Stevie and Carra, Mascherano, Torres and many other very good players, we just missed a little something.
"If you see the build-up of the team of Klopp, you see it progressing every time and it looks like it’s now coming to success also in the Premier League.