The Ukrainian winger looked set to join Liverpool in the January transfer window but the deal broke down on deadline day.
Tottenham Hotspur have since been linked with a move and fresh reports have suggested that new Manchester United boss Louis van Gaal is considering whether to pay his €15million (£12.1m) buyout clause.
Dnipro's sporting director Andrey Stetsenko has admitted that Konoplyanka's future remains uncertain but accepts it will be difficult to keep hold of such a talented player for too long.
Stetsenko says the 24-year-old would have no problem staying at Dnipro for now, although the club are taking no chances and have begun to search for other players in case he leaves.
"Our scouts are working to find his replacement. Sooner or later Konoplyanka will leave Dnipro," said Stetsenko, quoted in the Guardian.
"We know that English, Spanish and German clubs are monitoring the situation and are interested in the player. But we have had no offers.
"His contract has a buyout clause worth €15m for foreign clubs. For Ukrainian clubs the buyout is more.
"Konoplyanka spoke to me and said that if he did not have offers from foreign clubs in the future it would not be a problem. He would stay with us with pleasure and continue to play for Dnipro."
It is reported that scouts from Manchester United and Bundesliga club Schalke were at Dnipro's game against Metalurg Donetsk on Sunday.
Liverpool continue to be connected with Konoplyanka, but Stetsenko has suggested that their interest has cooled since January.
"After negotiations in the winter Liverpool did not contact us further about Konoplyanka," he said.