Brendan Rodger came within arm's length of landing the Ukraine international in the January transfer window, only to see talks break down at the 11th hour.
Now the Anfield boss is set to turn his attention towards other targets as he looks to prepare Liverpool for the rigours of Champions League football.
The only other club to have shown an interest in the in the 24-year-old is Tottenham Hotspur, but new boss Mauricio Pochettino is again looking towards other targets in the pursuit of a top four finish.
Konoplyanka currently has a £12m release clause in his Dnipro contract and Louis van Gaal is seriously considering whether or not to activate it this summer.
Van Gaal is unimpressed by the currently selection of wingers currently plying their trade at Old Trafford and wants to boost his options ahead of his debut season in charge.
Nani is set to leave the club while the future of Ashley Young, Wilfried Zaha and Antonio Valencia remains in some doubt.
Konoplyanka is reportedly willing to join Manchester United despite the fact that no Champions League football will be on offer next season.