The 20-year-old Serbian international joined the Reds earlier this summer for a fee of £20m.
Despite the club paying out an impressive fee for the youngster, Markovic is ready to embrace the challenges ahead of him at Anfield.
"I'm not afraid of challenges," he told the Liverpool Echo. "I'm not the most expensive signing of the summer but even if I were I wouldn't care much about that.
"I believe Liverpool fans expect a lot from me, and to be honest I expect a lot from myself. The same applies for the people who worked hard to bring me here."
Markovic could make his debut for Liverpool on Monday when they travel to champions Manchester City in the Premier League.