Konoplyanka is currently plying his trade for Dnipro, and would offer Reds boss Brendan Rodgers some new attacking options.
He is comfortable operating on either flank, or behind the striker, and is likely to cost in the excess of £15million.
The Reds seem to have turned their attentions to the 24-year-old after missing out on Mohamed Salah, who joined Chelsea at the eleventh hour for £11million.
Reds boss Brendan Rodgers revealed he remained hopeful the club would complete a ‘major signing’ before Friday’s transfer deadline.
Speaking after his side’s 4-0 thrashing of city rivals Everton, Rodgers said: “Hopefully we can have a major signing before the window shuts.
“I think we will hopefully do something over the next couple of days.”
Konoplyanka produced a couple of eye catching performances against England during the previous World Cup qualifying campaign.
He hit a superb long range strike in the 1-1 draw at Wembley in September 2012, and then gave Kyle Walker a torrid time on the left hand side as the rematch ended in a goalless draw in Kiev 12 months later.
Rodgers admitted last night he would be disappointed not to add any new additions before the deadline, but insisted he was happy with the support he was getting from owners, Fenway Sports Group.
“It couldn’t be further from the truth that I am angry with the club,” he added.
“I came here to do a collective effort to turn around the fortunes of the club.
“The people here are very important to what we are doing and we want to do it together.”