Klavan underwent a medical in Italy on Friday ahead of a £2m move to Calgiari, hours before the close of the Serie A transfer window.
Klopp refused to confirm Klavan’s impending exit on Friday but suggested that other players could follow the Estonian out of Anfield if the price is right.
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The Liverpool manager also said that all player departures rely on his approval and that if he wanted a member of his squad to remain on Merseyside, they would.
“No player would leave if I would not allow it,” Klopp said. “If he leaves, then I said yes. That’s how it is.”
On Klavan, Klopp added: “First of all, I didn’t hear that anything is finally sorted but I said before in general, it’s possible players will leave.
“If that happens, there will be always good for all three sides [the player, Liverpool and the buying club]. That’s the target. We will see what happens.”
Liverpool are willing to listen to offers for Simon Mignolet, Divock Origi and Lazar Markovic, who could all still leave before the close of the European transfer window on 31 August.
Klopp said any further departures will depend on the respective offers and stopped short of saying how many players he is willing to let leave.
“It’s about the situation. How is the offer? First of all, it’s about the need for us,” he said.
“lf he wants to leave, can we give him the opportunity or not? Then there’s an offer, and whether it’s an acceptable offer or not.
“That’s maybe the problem with the transfer window. We close in England and all the European world was waiting for the moment to try to get good football players. We are not in a financial need situation to do that.
Klopp added: “I want a good squad together. The more players the better. We could give a few players the opportunity [to leave], but we have to see how many. There’s no number in my mind at the moment.”
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