The Frenchman refused to join the rest of the Gunners squad on their pre-season tour of the USA after insisting he wants to leave.
The 33-year-old club captain has been linked with a move to Ligue 1 sides Girondins Bordeaux and Olympique Lyonnais.
Emery had labelled him an “important player” earlier this week but has now openly admitted Koscielny could leave.
When speaking about which players in his squad could step up and become captain, he said Koscielny could well leave, while insisting an English player would be ideal.
“I want one English player in these five captains,” he said. “Last year Xhaka, Mesut and Nacho were working as captains.
“But after Aaron Ramsey and Petr Cech left – and possibly Laurent Koscielny – I will want more.
“An English player who grew up in our academy can understand the English spirit and Arsenal values. These are the qualities and more [we want].
“We lost some players with big experience and a long time in England and Arsenal like Cech and Ramsey. We lost Koscielny too. They started one day being captain when they were young.
“We have young players with experience, players starting for the first time to be considered as captains. If we decide on a player they have the capacity and deserve to have the opportunity to be captain.
“(I look for) experience of leadership, being an example on and off the pitch, character and communication with the coach and other players, capacity to speak and to be there for supporters, a good connection and communication with the club.”
And Emery mentioned that Rob Holding could step up for the captaincy.
“We are really happy with his [Holding’s] progress. We need his performances as a centre back.
“[Before] he had his injury he was really playing with big performances.”
The only other English senior players in the squad are Calum Chambers, who spent last season on loan at Fulham, and fringe right-back Carl Jenkinson.
Meanwhile, Arsenal take on Fiorentina on Saturday night in the next pre-season tour game in the USA before facing Real Madrid on July 24.