Real Madrid have made an offer to make the France international, 25, their highest-paid player on more than £400,000 a week. And Klopp has suggested Liverpool will not be rivalling Los Blancos for Mbappe because of the finances involved.
That's despite the fact the Reds have previously had contact with the player's representatives, and the forward has hinted publicly that the Reds would be a club of interest to him. Klopp said: "Obviously, I'm not involved in that, but I can tell you I'd be surprised if all the top clubs were.
"The top clubs I know, for most of them it will be tricky - wages, signing-on fee." Liverpool already have a superstar in their squad in Mohamed Salah, who is fit again after a rare injury.
Kylian Mbappe is expected to leave PSG to join Real Madrid (Image: GETTY)
And Klopp has suggested he could unshackle Salah against Brentford today (12.30pm). Due to the Africa Cup of Nations and injury, the Egyptian with 18 goals and nine assists hasn't played since New Year's Day.
The German claims that Salah has been "on fire" in training and said: "There's no doubt about that, I'm over the moon that Mo is training and he looks really sharp. Thank God we did the job [without him], but having him available is a massive boost, on and off the pitch, definitely.
"It's nothing to do with the numbers he produces, just his personality and the guy, he's on fire. He wants to get started immediately and so yeah, let's see. It's all good."
On Salah's longest injury lay-off as a Liverpool player, Klopp added: "Obviously, he missed football a lot. It's probably the longest period he's been out for a long, long time, at least, I'm pretty sure since he's been here.
"So it was a really strange situation for him and for us to play without him for that long. It's been difficult. In the beginning it was especially difficult because of all the discussions in Egypt, he was injured, not making it up or whatever.
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Mohamed Salah is fit again for Liverpool this weekend (Image: GETTY)
"Everybody believed it in the moment he didn't play for us and thought 'Oh, it seems to be really bad'. So until then, I can't imagine what it's like for a guy who's always available and then for once you're not available and everybody's crying that you should be available.
"It's like OK, sorry, he's still human. But that's now already three or four weeks ago. Remember when we spoke about it if Egypt reached the final, then he might have a chance, but we didn't know this in that moment.
"Now he's back so that's good and definitely for him, it's a real challenge. He's always how is, he's the most professional player I’ve ever met. He dealt workload-wise really well with it, he used it. Let's see what he produces."