The 33-year-old French centre back, who has a year left on his contract, has been linked by the British media with a switch to Ligue 1 clubs Girondins Bordeaux and Olympique Lyonnais.
Arsenal fan groups call on Kroenke to reinvigorate flagging club
"I spoke with him three times for his situation. We wanted him to come with us but he decided to stay," Emery told a news conference after Arsenal defeated Colorado Rapids 3-0.
"For me now, it's clear. We need to keep moving ahead. We're playing with the spirit to create a new way." Emery said Koscielny, who joined Arsenal from French side Lorient in 2010 and has made over 350 appearances, was still an "important player".
"Now it's a matter for him and the club," the manager said. "They need to speak and are speaking about his situation ... I'm waiting on his conversation and decision ... I can't say more than that."
Koscielny rebellion adds to Arsenal gloom
Arsenal take on Bayern Munich on Wednesday, before matches against Fiorentina and Real Madrid as part of the International Champions Cup. Emery's side, who finished fifth in the league last season, kick off their new campaign at Newcastle United on Aug. 11.
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