The France international striker, who is set to be out of action until the new year with a foot injury, is expected to put pen to paper on a two-year renewal, with his previous agreement having been set to expire in 2016.
Speaking at a press conference ahead of Arsenal's UEFA Champions League clash with Galatasaray on Wednesday, Wenger revealed that the details were close to being finalised.
"It is done," he said. "We will announce it when it is completely finished.
"We want stability and want to keep the core of our team together. Giroud is an important player here."
Giroud has scored 41 goals in 102 Arsenal appearances in all competitions since joining from Montpellier in June 2012 for a reported fee of around £12 million.
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