The 20-year-old is set to move to Anfield for around £19.8m.
Serb Markovic has earned high praise in the Portuguese League for some standout performances and has long been linked with moves to both the Reds and Chelsea.
Now it seems that Brendan Rodgers will make the youngster his fourth summer signing after Rickie Lambert, Adam Lallana and Emre Can all joined the club in recent weeks.
Markovic is not seen as a direct replacement for Luis Suarez, who seems destined to join Barcelona this week, and Rodgers will still hope to bring in a top class striker as well as a central defender and left-back before the transfer window closes.
Alexis Sanchez is thought to be cool on a move to Merseyside, with Arsenal and Juventus his preferred destinations, leaving Rodgers still searching for a world class player to build another assault on the Premier League title around.
Southampton defender Dejan Lovren is keen to push through a move to join Lallana and Lambert at Liverpool, while Rodgers is expected to rekindle his interest in Sevilla's Alberto Moreno at left-back.
