The 24-year-old is understood to have been identified initially as a target for the summer but Liverpool are assessing whether Dnipro can be convinced to sell now.
Such a deal would demand a fee of £16m and last night there was speculation that Tottenham Hotspur had matched the offer made by their Barclays Premier League rivals. That will cause some consternation at Anfield since the club have missed out on long-term target Mohamed Salah, who last week signed for Chelsea.
"The information about a transfer to the English club is true," said Konoplyanka's father, Oleg.
The Merseyside Police and the FA have, meanwhile, opened investigations into allegations that a coin was thrown at Luis Suarez during Liverpool's 4-0 derby win over Everton on Tuesday night.