Klopp has previously said there will be new additions beyond just Naby Keita, who makes the move from RB Leipzig this summer, with a deal having been struck last summer.
He added: "We are going to think about what we achieved, enjoy the moment first". The future of any player is not important.
"That's what we are trying to do, create our own history", he stated.
Cristiano Ronaldo has now won five in his great career, but even he could not argue that this was Bale's evening.
The Portuguese global has a new contract pending so post-final talks were always going to take place.
"He is able to deliver an atmosphere where everyone is relaxed but focused enough and this is why I'm pretty confident they have a chance".
"I know Florentino Perez pretty well and he's a sharp businessman", he exclusively told Starsport. It is something extraordinary. I don't want to take over from the unique moment of my teammates who deserve it, who are real champions.
"I'm sure Madrid have great fans too but hopefully ours can create an atmosphere similar to at Anfield because it's made a big difference to us".
"I had talks with other clubs and they didn't sound like a football club".
Madrid will be desperate to keep their man as they look to continue their dominance over the rest of Europe.
Liverpool manager Jurgen Klopp has challenged his players to stop Real Madrid lifting a third consecutive Champions League trophy on Saturday and show fans that winning "big things" is still in the club's DNA.
The German keeper had earlier handed Real a 51st minute lead when he threw the ball straight at striker Karim Benzema and the ball rolled into the unguarded net off the Frenchman's leg.
After allowing a completely legitimate goal to Gareth Bale on a spectacular bicycle kick, the demons returned for Karius on another ball from Bale later in the second half.
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