The Serbian has already sent a message to the Benfica fans, which said: “Thank you for everything and goodbye.”
And Sky Sports reporter Vinny O’Connor said on Monday afternoon: “Lazar Markovic is all set to become Liverpool’s fourth summer signing.
“He has just left Liverpool’s training ground in a club car but he is expected back later to complete the formalities of the medical.
“It is a deal which could drag into tomorrow but the club are hoping to announce today that he is a Liverpool player.”
The 20-year-old Markovic can play out wide or as an orthodox striker, and has already been capped 12 times by Serbia.
Having begun his career with Partizan Belgrade, he helped Benfica to the Portuguese league title last season.
However, he missed the Europa League final defeat to Sevilla through suspension, having been sent-off during injury-time in the second-leg of the semi-final against Juventus.
He had already been taken off in the 0-0 draw but was dismissed for scuffling with Juventus substitute Mirko Vucinic.
Markovic is now poised to follow Rickie Lambert, Adam Lallana and Emre Can, who have all signed for Liverpool since the conclusion of the 2013/14 campaign.
But the Reds have parted company with last season’s top scorer Luis Suarez, who is to join Spanish side Barcelona.