The Benfica winger has been on Merseyside to undergo a medical and it's understood a deal is likely to be finalised on Tuesday.
His arrival will take Brendan Rodgers' spending close to £60million after Liverpool triggered the 20-year-old's £20million release clause just a year after the Serbian moved to Portugal.
Rickie Lambert, Adam Lallana and Emre Can have already been added to the squad while negotiations are continuing in an attempt to sign Belgium's Lille striker Divock Origi.
Rodgers is looking to strengthen further following the £75million departure of Luis Suarez to Barcelona, which is expected to be completed later this week.
Reds forward Iago Aspas has returned to Spain on a year-long loan with Sevilla after a disappointing maiden season having moved from Celta Vigo last summer.
The Spanish outfit announced the clubs had agreed a loan deal, with the option for them to sign Aspas on a permanent deal.
Aspas' departure may help in Liverpool's pursuit of the Spanish left-back Alberto Moreno.
The two clubs appeared to have reached an impasse over the defender's fee, with the Merseysiders unwilling to meet a £20million valuation, but talks have continued.