The Europa League winners were hoping to lure the ??15million-rated Konoplyanka, who is a free agent this summer, to the Sanchez Pizjuan stadium but negotiations have proved unsuccessful.
According to a recent report in The Mirror, Newcastle and Stoke are interested in a move for the Ukraine international, while he has also been linked to Tottenham by several media publications.
“We set ourselves a deadline to sign Konoplyanka and it has expired,” Sevilla sporting director Monchi said on his club’s official website.
“We have ruled out this possibility and we are now working on other options that we feel could be sufficiently valid to cover that role. We need to keep planning our season.
“We have not reached an agreement due to negotiation reasons but this club is important enough to set itself deadlines and once those expire, we must move on and think of other alternatives.”
Monchi confirmed Sevilla are in talks to sign AC Milan defender Adil Rami.
The France international joined Milan from Valencia last year but started in just 18 Serie A games for the Rossoneri and is reportedly keen to leave the Italian club this summer.
Rami, 29, is also a reported target of Manchester United and Lyon.
“It’s not going to be easy,” Monchi said. “He is in a big club like AC Milan but also because he has a lot of suitors.
“But we are enthusiastic that we have the opportunity to try to sign him.
“Once again, as was the case with Konoplyanka, we are not going to wait forever. We also have set ourselves a deadline.”