The 23-year-old winger was seen as one for the future when he arrived at Anfield in 2014 from Benfica, but injuries hampered his progress on Merseyside.
Markovic spent much of his time out on loan at Fenerbahce, Sporting CP and most recently Hull, having not played at all for Klopp in the past two seasons.
The German coach said the Serbia international is now free of injury, but does not feature in his future plans for the English giants.
“With Lazar, it’s no secret that if he finds a club then we will negotiate,” Klopp told the Liverpool Echo. “It was like this last year too.
“He’s a really good player. I like him as a person. He’s now fit and another one who is in the best shape since I’ve known him.
“Before he had problems with his groin but now he’s good. There will be a club out there who needs him.”