Spurs looked to be in a position to hijack the Reds' deal for the highly-rated Ukraine international, but have pulled the plug after coach Tim Sherwood expressed doubts
The Reds are understood to have made a more attractive financial offer to both Dnipro Dnipropetrovsk and the player, as Brendan Rodgers looks to boost his side's hopes of a top-four finish in the Premier League.
Liverpool managing director Ian Ayre reportedly flew out to Ukraine on Wednesday to push through the deal - and the Merseysiders' are now close to landing their man.
The Anfield outfit is desperate to force the move through after being gazumped by Chelsea in its atempts to sign Mohamed Salah from Basel.
The pacey 24-year-old plays on the left side of attack and is also highly rated by Tottenham technical director Franco Baldini.
However, while Spurs coach Tim Sherwood admires Konoplyanka, he has concerns about how the player would adapt to the Premier League and he would prefer to wait until the summer to land other targets.
Tottenham is notoriously unpredictable in the latter stages of the transfer window, but senior sources at the club do not expect Spurs to sign Konoplyanka, with former White Hart Lane favorite Dimitar Berbatov the most likely arrival before Friday's deadline.
Konoplyanka is eager to move to England and has been tracked by a number of Premier League clubs, including Manchester United, since his impressive displays at Euro 2012.
Rodgers wants to improve his squad and will be anxious to push the Konoplyanka deal over the line on Friday.
"I think we will hopefully do something over the next couple of days," the Liverpool boss said earlier this week.
"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."