“I will say at the start of pre-season, ‘Welcome, and then it’s up to you’,” Klopp was quoted as saying in the Express.
“That is how it is in football, it is a long preseason and if he wants to come back to Liverpool on July 2, then you are welcome.”
Klopp also underlined that the current team is short on wingers and that a wide-player like Markovic could be a welcome addition over the summer.
“We are short on wingers. Everybody who is involved in pre-season can have a part to play,” he added.
The Serbian international is current in Liverpool holding talks with the club over his future.
Markovic faced an uncertain future after struggling to settle in last season under the stewardship of Brendan Rodgers and was sent on loan to the Yellow Canaries.
The 21-year-old has established himself as a first-team regular at Fenerbahce and the Istanbul giants are reported to be keen on keeping Markovic on a permanent deal or another one-year loan.
Markovic has missed the last few weeks with injury but is expected to return to the side next week after making a recovery.