The Reds reportedly made a bid of around £19.8million on Saturday night which was accepted by Benfica, although there has been no official confirmation from either club.
Chelsea reportedly have an option to match Liverpool's bid for the 20-year-old Serbia international, but they have apparently shown no interest at this stage.
Markovic, who has made 12 appearances for Serbia, joined Benfica from Partizan Belgrade just over a year ago and made a big impression last season.
If he moves to Anfield he will join Rickie Lambert, Adam Lallana and Emre Can as new arrivals at the club this summer as speculation grows that Luis Suarez will leave for Barcelona.
Synergy and yet we beat you without the nippy racist last season. Studge scored the winner. If you think that Pool will drop off a cliff like Utd last season then you're deluded. How many teams out-played us last season? That control over a game was not down to Suarez alone. Rodgers has developed a style of play that will make Pool a very hard team to beat again this season. Add Lovren to that defence and bring Enrique back in with Johnson out and you have the makings of a very strong team at home and abroad.- thesza888