The midfielder is set to join permanently in the summer.
The midfielder joined the Reds in the January transfer window but was loaned back to Red Star Belgrade until the end of the season.
He is a relative unknown, but Jurgen Klopp reportedly beat off interest from across Europe to make the youngster his first signing at Anfield.
But it seem the German wasn’t the only one convincing him to move to England, with Markovic also providing a ringing endorsement of the club.
“I spoke with Lazar Markovic and he told me good things about the club,” the Liverpool Echo reports him saying.
“He told me that Liverpool is a great club, that the pressure and expectations are enormous, and that the first two or three months are the most important.”
“I will have to prove myself during that period and show my qualities. I will have to show what I am made of. I am very confident.”
Grujic will now be hoping he can have a more positive first year at the club than Markovic did.
There was great excitement when then the Serbian joined in a big money move from Benfica, with many predicting he could be a future star in the side.
Instead he struggled to establish himself in the first team with a series of disappointing displays under Brendan Rodgers as the Reds slumped in general.
Indeed he was one of several disappointing signigns that summer, and Grujic will be hoping he doesn’t follow a similar path to his fellow Serbian.