The France defender opted out of the Gunners' pre-season tour of the United States, according to Emery - who stated he will instead work with "players that want to be here".
"I tried to continue working and finding one solution between the club, between him and us," Emery told arsenal.com after a penalty shoot-out loss to Real Madrid in a pre-season clash in Washington.
"When he decided not to come here with us on tour, the solution is now only for the club and him.
"He decided to be out. I respect him but I have a responsibility, he has a responsibility, and the club have their responsibility.
"Now it's an issue only for the club and him. My idea is to continue with the players we are working with, and the players that want to be here."
Koscielny, 33, signed from Lorient in 2010 and has since played over 350 games for Arsenal, scoring 27 goals and being named club captain last season.
He has been linked with several clubs back home in France, with Bordeaux coach Paulo Sousa confirming an interest but Rennes president Olivier Letang insisting his club have not been in contact since a tentative enquiry in early June.
