Lunin is expected to join up with his teammates for pre-season, when Julen Lopetegui, who was recently confirmed as Los Blancos' successor to Zinedine Zidane, will decide where he fits into the pecking order at the Santiago Bernabeu, although it's unlikely he will displace Keylor Navas in his debut season at the club.
The 19-year-old has spent his career in Ukraine playing for Metalist Kharkiv before he left to join Zorya Luhansk in 2016. He's made 51 appearances over the past two seasons, registering 20 clean sheets in the process.
Following his impressive form in the Ukrainian Premier League, Lunin was called up to the national team in March and made his international debut against Saudi Arabia in a 1-1 draw.
According to another Marca report, despite Lunin's imminent arrival, Real Madrid remain interested in Roma and Brazil goalkeeper Alisson Becker, who has also been heavy linked with a move to Liverpool.
The 25-year-old is said to be valued at around €70m (£61.5m) by I Giallorossi, although Real are confident that a €60m offer could persuade the Serie A side into parting with their prized asset.
Alisson, Brazil's starting World Cup goalkeeper ahead of Manchester City's Ederson, arrived at the Stadio Olimpico from Internacional in 2016. His outstanding form this season has seen him shoot to prominence, with a number of clubs from around Europe keen on acquiring his services.