Markovic was brought back from his loan at Sporting Lisbon earlier this month before being sent straight on loan to Hull.
He made his debut for The Tigers in their EFL Cup match against Manchester United on Thursday after coming off the bench and assisted Oumar Niasse's winner but couldn't help Marco Silva's side reach Wembley.
The 22-year-old is yet to play a minute of competitive football under Jurgen Klopp at Liverpool who sent the winger out on loan in the summer.
Jurgen Klopp says Lazar Markovic could return to Liverpool
Lazar Markovic is currently on loan at Hull
Having suffered injuries in his loan spells at Fenerbahce last season and Sporting Lisbon, Markovic will be hoping he can begin to revive his career in the Premier League.
And Klopp hasn't ruled out Markovic playing for Liverpool again.
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“Why should I say now no chance for Lazar Markovic? Why not," said Klopp.
"He’s still a young boy. He has struggled with injuries.
“If he can stay fit and help Hull then it’s easier for us to look at how he’s doing.”