The Reds opened negotiations after Ian Ayre flew out to Ukraine earlier this week but are struggling to agree a fee for the 24-year-old winger before Friday's 11pm deadline.
As revealed , the left-sided attacker has set his heart on a move to Liverpool after Tottenham pulled out of a deal, but Dnipro are keen to secure a sale for as close to their £20m valuation as possible.
But Oliver Cabrera, who owns OML Sports & Marketing, the company Konoplyanka is signed to, told Goal: "We have a very good relationship with the president [Ihor] Kolomoyskyi and he doesn't want to sell the player."
"Yehven and his father respect that so a move is very unlikely."
Cabrera is one of the main parties negotiating the deal from his base in Stockholm, and did insist that the proposed transfer has not collapsed completely.
Liverpool are desperate to force the move through after being gazumped by Chelsea in their atempts to sign Mohamed Salah from Basel.
Tottenham pulled out of the race to sign Konoplyanka after Tim Sherwood had concerns over how well the Ukraine international would adapt to the Premier League
"There's obviously an interest in the player but there's no update," Brendan Rodgers said at his Friday press conference.
"The staff over there have done brilliant work with regards to trying to get the player.
"But we need to see how that develops over the course of the day. It's all happened so quickly and the deadline is tight.
"We've had a list with a number of players on it, so we'll see how it develops later."
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