Markovic, 20, starred as Benfica narrowly missed out on a historic quadruple last season and now looks set for a move to the Premier League.
Reports in Portugal put the expected transfer fee at 25m euros (£19.8m).
Liverpool manager Brendan Rodgers has already bolstered his squad by signing midfielder Emre Can from Bayer Leverkusen and Southampton duo Adam Lallana and Rickie Lambert.
Striker Luis Suarez – who is currently serving a four-month ban from all football-related activity for biting – has been heavily linked with a big-money switch to Spanish giants Barcelona.
- Sports & Recreation
- Bayer Leverkusen
- Adam Lallana
- Luis Suarez