The Serbia international winger arrived at Anfield in a reported £20 million deal from Primeira Liga champions Benfica after impressing in his one season in Portugal.
Markovic has made just two Premier League starts since moving to Merseyside, with Liverpool boss Brendan Rodgers choosing to bed the 20-year-old in slowly.
The former Partizan man has no complaints, though, and is keen to fully acclimatise to English football.
"You know how things go in football, I'm getting there and adjusting well," he told Serbian newspaper Mondo.
"It will take a little more time but, all in all, I feel okay.
"I feel great there and everybody has been great with me. I could not wish for more. I'm happy and that is the most important thing.
"My team-mate is the legendary Steven Gerrard, the fans love me and Anfield is great. But, as I said, I just need a little bit more time."
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