Promes was linked with Liverpool over the summer.
Asked about Liverpool's interest in Promes, Klopp said: "He's a good player, a very good player but there's nothing else to say. There are a lot of good players that we have already.
"We already have a Dutch player (Gini Wijnaldum) who knows him really well so obviously they are good friends but this is not the place to talk about this.
"He's a good player but a Spartak player."
Informed that Spartak manager Massimo Carrera had named Promes as a major doubt for the game, Klopp added: "He didn't play in the last game or two, I'm not sure. He's a very good player.
"He has speed, he's good on one v one situations and all that stuff, so of course that's a weakness.
"It's the same for each team, we played the last three games without Sadio Mane, also a very good player.
"He's not the only good player in the Spartak team but he's a very good one. But it's how I said it always affects performances but we will not win because one player is out and Spartak won't win because one player is in on our side.
"We have to play together and that's what we try . I don't know if Quincy can play or not but the analysis we did was already without him as he didn't play in the last game."