Klavan who is believed to be close to joining Cagliari in a £2m deal.
The 32-year-old is due in Italy today for a medical and to negotiate personal terms.
But Klopp says: "I didn't hear that anything is finally sorted.
"But I said before it's possible players will leave the club and if they do it will be good for all three sides.
"No player would leave if I did not allow it. If he leaves then I said yes to it, that's how it is."