The Anfield club have seen several targets slip from their grasp in the past two transfer windows, from Willian to Henrikh Mkhitaryan and most recently Mohamed Salah.
But Le 10 Sport claims Paris Saint Germain, who have been long term admirers of the Ukrainian winger Konoplyanka, will not act on their interest in the midfielder giving Liverpool a free run.
The defending Ligue 1 champions have not been getting the expected production from Jeremy Menez, Javier Pastore and Lucas Moura this season.
And they reportedly viewed Konoplyanka as potentially another option out wide for Laurent Blanc.
The report notes that British media claim Liverpool are closing in on a deal for the Dnipro star, but it warns that PSG are still tracking the 24-year-old wide-man.
Valued at €19m by his club, Konoplyanka impressed scouts against England in the World Cup qualifiers and watching French scouts against France in his country's World Cup playoff match last November.
Paris Saint Germain confirmed the capture of Yohan Cabaye from Newcastle earlier this week.