Arteta has entered the final year of his current deal, leading to some concern among Arsenal supporters despite the Spaniard repeatedly making it clear that he is happy at the Emirates Stadium.
Garlick has now moved to calm those concerns, insisting both Arteta and Arsenal want to continue working together.
"Mikel wants to be at Arsenal and we want Mikel at Arsenal. It's only a matter of time before we put that into a new contract," Garlick told the BBC.
"Everyone is very confident and calm. We're just navigating a transfer window and I'm sure Mikel's contract will be resolved very shortly."
Arteta has transformed Arsenal since taking charge in 2019 and last season ended the club's 22-year wait for the Premier League title. He also guided the Gunners to the Champions League final.
The 44-year-old signed his previous contract extension in September 2024, but Arsenal now appear close to securing his long-term future.
The new agreement is expected to be completed after the current transfer window closes.
Arteta will begin Arsenal's title defence on Friday when the champions host promoted Coventry in the opening Premier League match of the season.
