"We have a very good relationship with the president and he doesn't want to sell the player," agent Oliver Cabrera said.
"Yehven and his father respect that so a move is very unlikely."
Former Arsenal and Ukraine defender Oleg Luzhny had earlier cast doubt over Konoplyanka's ability to settle in the Premier League.
"When you play in the Ukraine, you can afford not to run," Luzhny said.
"In the match against France, it was evident that Konoplyanka barely runs at all. Konoplyanka is a good player, but he is suited to Spain or Italy, not England.
"I don't think the English league is right for him. The game in England is totally different - it's about power. You have to run back and forth, back and forth.
"You run at speed up and down, and it's like that for 90 minutes."
Spurs, rumoured to be in contention to sign the Ukrainian, have since pulled out of the race.
When asked what percentage he would put on them signing anyone before the Friday night 11pm deadline, the Tottenham manager Tim Sherwood said: "Zero."
"Daniel (Levy) asked if I want to strengthen in this area or need any help, but I'm confident with the players we've got," he revealed.
"I don't need anyone else, thank you very much."
Reds managing director Ian Ayre has been in Ukraine for a number of days hoping to broker a Amazon Deal Online for Dnipro's 24-year-old playmaker and believed he was close to concluding the transfer until Tottenham entered the race.
If the Reds are to succeed, they will need to part with at least £15m.
Konoplyanka is rumoured to earn in the region of £100,000-a-week and talks were ongoing with the Ukrainian club, who are bankrolled by billionaire owner Kolomoyskyi.
Rodgers is especially keen to sign the midfielder after missing out on Mohamed Salah to Chelsea last week and has ordered Ayre to prioritise the deal above everything else.
"There is no update yet," Rodgers said. There is obviously an interest in the player, but there is no update.
"We'll see how it evolves. It is obviously a little complicated, but the staff that are over there have done brilliant work in terms of giving us every chance to get a player.
"So we will just have to see how that develops over the course of the day.
"It has all happened very quickly. Obviously the timeline on everything makes it tight."