Markovic is spending the second half of the campaign with Hull City, having seen his initial spell with Sporting CP cut short in January.
Before that, the 23-year-old turned out for Fenerbahce throughout 2015/16, though he made just 21 appearances for the Turkish side, with his season hampered with injury.
“I’m more mature and I have more experience and that is going to play quite a big role in my development.
“We will have talks in the summer and see how it goes from there.
“I think [Klopp’s style suits me] but it’s a different question for me and a different question for the coach.
“It does suit the style of Liverpool, the supporters seem to like it and the players seem to enjoy it so it’s good all round.
“Of course, every experience at every big club in every big city builds experience and maturity. I’m sure that will help in the future.”
Markovic’s future on Merseyside is certainly in doubt, particularly given Klopp allowed him to join the Tigers despite a dearth of attacking options at his disposal in January.
The German is still in search of reinforcements out wide, however, and speaking after the winger’s move to Hull, he suggested the door was not yet closed on Markovic.
“He’s still got a contract, so why should I say there’s no chance for Lazar Markovic?” he asked.
“If he plays really well at Hull, then why not? He’s still a young boy.
“We all know we struggled because of a few injuries, in the wrong moment.
“If he can stay fit, and help Hull, for us it’s easier to look than at what he was doing in Portugal.”
Whether this is a mere public showing of support, much as he has offered to Crystal Palace loanee Mamadou Sakho, remains to be seen.