The Serbia international arrived at Anfield in the summer of 2014 from Benfica, costing the Reds a reported £20million.
But the 21-year-old struggled to adapt to life in England and found first-team opportunities hard to come by, starting just 11 Premier League games last term.
Markovic left the Merseysiders last summer to join Turkish giants Fenerbahce on a season-long loan following his difficult start at Anfield.
And the former Partizan Belgrade winger, who has two goals and three assists to his name this term, admits he wanted to leave after falling out with then-manager Rodgers.
“I had no problem with Brendan Rodgers and we had a bond until, for some reason that remains a mystery to me, he changed,” Markovic told Turkish newspaper Fanatik.
“He stopped playing me and then at the start of the season he didn’t even include me in the squad, and nobody explained to me what was going on or what his plans were, so I decided to leave.”