Chief executive Ian Ayre had flown out to Ukraine to continue negotiations about a deal, thought to be in the region of £15m, but the move looks to have fallen apart in the final minutes of transfer deadline day.
Konoplyanka is believed to have undergone a medical, but unconfirmed reports suggest the deal fell through because Dnipro president Ihor Kolomoyskyi refused to sign the necessary paperwork - despite the £15m release clause being met.
Premier League rivals Spurs were also interested in Konoplyanka, but he will now remain with Dnipro.
The medical was completed in Ukraine as Konoplyanka, who scored against England at Wembley during World Cup qualifying, does not currently have a visa.
Liverpool manager Brendan Rodgers had said earlier on Friday: "There's obviously an interest in the player.
"We'll see how it evolves. It is obviously a little complicated but the staff that are over there have done brilliant work in terms of giving us every chance to get a player."
Konoplyanka also claimed to be 'excited' by the possibility of joining Liverpool - but talk of a move failed to materialise as the transfer window closed at 11pm on Friday.
The failure to sign Konoplyanka means Liverpool have failed to sign the winger that Rodgers wanted to bolster his side's push for a Champions League place - they also lost out to Chelsea in the race to sign Mohamed Salah.
Rodgers was also quoted as saying on the club's official website: "If you look at the position we're in with 15 games to go, we have shown consistently that we have the squad to compete.
"The benefit of the second half of the season is that there is still a lot of development left in a lot of our young players."