Brendan Rodgers is looking to bolster his attacking line as he chases Champions League football and has lined up the Ukraine international after missing out on Mohamed Salah.
Dnipro is hoping to secure a fee of 24 million euros for winger Konoplyanka, who hit the headlines in England following his terrific long-range strike against the Three Lions in a World Cup qualifier back in 2012.
Liverpool is, however, reluctant to pay such a lofty fee and is looking to strike a deal around the €15 million mark as the club attempts to secure a signing late on in the window having missed out on Mohamed Salah to Chelsea.
Speaking after watching his side's 4-0 thumping of Merseyside rival Everton, Rodgers expressed his desire to seal a "major signing" before Friday's deadline.
"I think we will hopefully do something over the next couple of days," he told reporters.
"Hopefully we can have a major signing before the window shuts and if we can do that we will be set up for the remaining games."
Despite reports again linking Thomas Ince with a return to Anfield, Goal understands that the Merseysiders are not currently interested in the 21-year-old, who has been granted permission to leave Blackpool on loan in January.