Partey made a cameo appearance at the Etihad Stadium on Saturday as Raheem Sterling’s 23rd-minute goal gave Man City a 1-0 victory.
The Black Stars midfielder who joined the Gunners from Atletico Madrid on the European transfer deadline day, made his Premier League debut after replacing Granit Xhaka in the 83rd minute.
Within seven minutes of his introduction, the 27-year-old received a yellow card for a challenge on Algeria star Riyad Mahrez.
Partey went into Saturday’s game after just one training session at London Colney and the Spanish manager is hoping to have him fully settled in North London in no time.
“Yes, we will see how quickly we can make it with him,” Arteta told the club website.
“I think we have to respect that process and that timing for him because he only trained for a day really and there’s a lot of new information and different game models for him to understand, and we have to respect that.
“But I think when he came on he looked good.”
Partey joined the Gunners last week after his international assignment with Ghana where he played in their friendly matches against Mali and Qatar in Turkey.
He will be hoping to make his full debut when Arsenal begin their Europa League campaign with an encounter against Rapid Wien on Thursday.
