The Serbian winger joined the Reds last week after the Anfield side met his buyout clause at Benfica, and the talented Markovic has been described as one of the most mouth-watering young prospects in European football.
In the absence of Luis Suarez next term, much will depend on the likes of Markovic, Adam Lallana and Philippe Coutinho to provide the creative spark for Brendan Rodgers, but Rui Costa thinks the 20-year-old has all the ingredients to succeed.
And as a technically gifted playmaker with 94 caps for Portugal, Rui Costa is more than qualified to give his verdict on creative technicians.
Benfica's director of foobtall told the Daily Mail: "I believe he will never forget the time he spent with us at Benfica. Markovic is a huge talent and I believe his speed and skills can make a difference in the Premier League. He's not a physical player, but he has the ability and the flexibility to escape defenders easily.
"Apart from that, he's a really focused player. He loves football and enjoys playing and watching the game. Markovic is also very cold blooded when he's in one to one and he's not afraid on facing the opponents. He's always eager to learning, so I think he will adapt himself very quickly.
"What I will remember most about the transfer is how thankful and emotional he was when we told him Liverpool had met his release clause and that was going to allow him to sign for Liverpool."
Markovic missed Thursday morning's 1-0 defeat to Roma, and the youngster is expected to make his bow on Sunday when the Reds take on Olympiacos in Chicago.
Rodgers has also added Adam Lallana, Emre Can and Rickie Lambert to his ranks so far to the tune of around £60 million, and Loic Remy is expected to join this week.
Deals for Dejan Lovren and Belgium international striker Divock Origi are also reportedly in the pipeline.