Liverpool managing director Ian Ayre flew out to Ukraine earlier this week to hold discussions regarding a deal for Konoplyanka.
Tottenham are also understood to have shown an interest in Konoplyanka, but Liverpool are in pole position to secure his signature.
Reports have claimed that Liverpool have upped their offer to £16million for the 24-year-old Ukraine international as manager Brendan Rodgers tries to finalise a 'major signing' before Friday's deadline.
Konoplyanka, who scored against England in a 2014 World Cup qualifier at Wembley in September 2012, is surprised at how strong Liverpool's interest has become.
"I'm excited about it and soon everyone will know where I will play," Konoplyanka is quoted in the Daily Star.
"Is it very serious with Liverpool? I am shocked myself at how serious it is. I think in the near future everything will become clear."
Liverpool missed out on the signing of Mohamed Salah earlier this month after the Egypt international winger opted to join Chelsea from Basel.
Yevhen Konoplyanka - Well it's a big name signing in the literal sense I suppose so Rodgers wasn't lying.- bamboo22