The 25-year old had to be helped off the pitch following a collision with Chelsea wing-back Victor Moses, and was due to undergo a scan to reveal the extent of the injury on Thursday.
But new head coach Unai Emery confirmed on the recent pre-season tour of Singapore that the forward was close to agreeing fresh terms.
In the same brief statement, on the club's official website, Arsenal also confirmed the status of Aaron Ramsey who missed the shootout win over Chelsea despite having initially been named in the starting line up.More news: Chloe Learey: Celebrating Breastfeeding Awareness Month
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'Sead Kolasinac sustained an injury to his left knee.
He could miss as many as eight Premier League games and two Europa League fixtures, with the Gunners setting a minimum recovery timeframe of eight weeks.
"I'm very pleased Alex has signed a new contract with us", he said in the club's announcement.
The Wales global midfielder is now a doubt for new Arsenal boss Unai Emery's opening Premier League game against Manchester City on August 12, live on Sky Sports Premier League.