Konoplyanka is available on a free transfer from Dnipro this summer and is reported to have been offered an attractive contract by Stoke, who are likely to face competition from clubs including Europa League winners Sevilla.
The Potters are also reported to have agreed a fee for Sporting Lisbon right-back Cedric Soares, and Scholes admits the club are now shopping in a different market to previously.
“The truth is that when you improve as a club – and there is no question we have improved a lot over the years – you raise the bar in the players you are going for,” Scholes told The Sentinel.
“The kind of players you target are aspirational players, players who are about pushing the boundary even more, so you are in competition with good clubs.
“We don’t want to be bringing in players who have no other choices. Perhaps barring the top three, four or half-dozen clubs in Europe, we are now in the market for that next level of player.”
Stoke also remain interested in re-signing Chelsea winger Victor Moses, who spent last season on loan at the Britannia Stadium, but Scholes has reported no progress on that front.
“Mark is on record saying that Victor did very well here and he is a player we would like to bring back,” Scholes said.
“But we have to bear in mind that he is a player who belongs to another football club at the moment.
“It’s Chelsea’s prerogative. They haven’t decided what they are going to do with Victor and whether or not they want to keep him. We will wait and see on that one.”