Goal understands that the Reds have started negotiations Dnipro over a deal for the Ukraine international, with Brendan Rodgers's men hoping to sign the winger for a fee in the region of £12 million after missing out on Mohamed Salah to Chelsea.
Oleg Konoplyanka admits that there is interest in his son from England and that he could be set to leave Dnipro for the Premier League before the close of the transfer window.
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"He can change clubs later this week. We do not consider offers from Ukraine."
Speaking after Liverpool's 4-0 victory over Everton in the Premier League, Rodgers confirmed that his side were keen to bring in a player in January.
"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."
Konoplyanka will be familiar to fans in England after hitting a superb strike against the Three Lions in a World Cup qualifier in 2012.