Saka seemed to injure his foot during the 4-0 win when blocking a shot with around 15 minutes to go.
Bournemouth left-back Milos Kerkez had a shot in the box and appeared to stand on Saka’s foot by accident as he followed through.
Asked post-match for an update on the England winger, Arteta said: “I don’t yet, as I haven’t had a chance to speak to him.
“I think it was a stamp in the same area but [Gabriel Jesus] was limping as well after the game so let's see how they are.”
Arsenal will hope Saka recovers quickly as they have two big games next week before the international break.
Jesus is another concern after he was injured following a mazy run near the end of the game, at which point Arsenal had made their five substitutions.
The Gunners travel to Lens in the Champions League on Tuesday night and then host Manchester City in the Premier League on Sunday.