Markovic was loaned to the Turkish Super Lig side last summer, with Brendan Rodgers seemingly not content with the development made in his first season on Merseyside.
The 22-year-old has since criticised Rodgers for the breakdown in their relationship, saying “nobody explained to me what was going on or what his plans were, so I decided to leave.”
But a change in hands at Liverpool has given Markovic a new opportunity, with Klopp having met with the Serbia international on his return to Melwood as part of his recovery from a groin injury.
After talks, Klopp admitted on Friday that he was welcome back at the club this summer.
“He’s injured so he is back for us. But he is not our player so he will have to go back [to Fenerbahce],” Klopp told reporters.
“We will talk about things, we will speak about next season while he is here.
“I will say at the start of pre-season, ‘Welcome, and then it’s up to you’.
“That is how it is in football, it is a long pre-season and if he wants to come back to Liverpool on July 2, then [he is] welcome.
“We are short on wingers. Everybody who is involved in pre-season can have a part to play.”
Klopp’s admission that he is lacking in wide options is an obvious one, with Jordon Ibe the only orthodox winger at his disposal in the Liverpool first team.
Markovic would provide the German with pace, energy and a direct brand of attacking football from the flanks, while also being able to interchange with the likes of Roberto Firmino and Philippe Coutinho in a fluid forward line.
Able to shine on the left or the right, Markovic can also perform as a second striker, but what will particularly endear him to Klopp is his work off the ball.
During his time with Fenerbahce, Markovic has showcased his strong work rate in pressing the opposition—a key feature of Klopp’s attacking blueprint.
The return of Markovic would arguably alleviate the need to sign another starting option in attack.
Though with reports linking the Reds with Bayern Munich’s Mario Gotze, it is likely that Klopp would take a patient approach to Markovic’s development.
In 20 appearances for Fenerbahce this season however, the former Benfica man has clearly shown Klopp enough to secure a role at Liverpool in 2016/17.