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.