The Benfica winger has been on Merseyside to undergo a medical and Press Association Sport a deal is likely to be finalised on Tuesday.
His arrival will take Rodgers' spending close to £60 million after Liverpool triggered the 20-year-old's £20m release clause just a year after the Serbian moved to Portugal.
Rodgers is looking to strengthen further following the £75m departure of Luis Suarez to Barcelona, which is expected to be completed later this week.
Sevilla have also confirmed they have agreed to take Liverpool forward Iago Aspas on loan for the season.
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