The Reds came within hours of sealing a deal for the 24-year-old in January, but saw their efforts to secure his signature thwarted by his club side.
Liverpool were believed to have agreed a contract with the player and carried out a medical, yet a fee could not be settled on with Dnipro Dnipropetrovsk, who are bankrolled by wealthy Ukrainian businessman Ihor Kolomoyskyi.
It has since been reported that Tottenham have moved into pole position for the £15m-rated wide-man, but now Brendan Rodgers is once again keen on him.
Unlike Spurs, the Merseysiders will be able to guarantee him Champions League action for next season, and negotiations should be smooth with the player having agreed to the move in the past.
Rodgers has a rumoured £60m+ to spend in the coming transfer window, which could help when it comes to sorting a fee with Dnipro.
As well as Konoplyanka, Liverpool may re-visit another old target in the shape of Henrikh Mkhitaryan, despite the fact they missed out on him last year as he signed for Dortmund instead.