The Estonia defender joined the Reds from FC Augsburg in the summer of 2016 and has since made 51 appearances for the club.
Klopp knows any agreement for Klavan to remain at Anfield beyond the length of his current deal must be convenient for all parties - but there is no doubt from his side.
"Yes, of course," the manager said of his hopes to retain Klavan's services.
"[He is a] fantastic player, really good footballer, he has all what you need. Of course I would but there are two sides to it."