The English club will look to make the signing official after they reached an agreement with Benfica over the transfer of the 20 year-old Serbian international.
According to Portugues source A Bola, both sides have agreed to close the signing for a fee of 25 million euros in order for Brendan Rodgers to get the player whom he was interested in last Summer.
Markovic made 26 appearances in the League last season for Benfica with the forward who is capable of playing on both flanks and also through the middle scoring 5 times and contributing 4 assists as well.
The former Partizan Belgrade player should be the English club's fourth signing of the summer with Southampton duo Adam Lallana and Ricky Lambert plus Bayer Leverkusen's defensive midfielder Emre Can all having already joined the club.