The Gunners brought in Gabriel Magalhaes and Thomas Partey for big money in the summer.
They also signed Willian on a free transfer and made other moves.
But Arteta wants to sign more players, and is particularly interested in Red Bull Salzburg star Dominik Szoboszlai, per Goal.com.
"We are planning, talking with Edu and with the club about the things we can do in January," he told reporters.
"At the moment it's pretty difficult, unpredictable as well in terms of places as we are very restricted at the moment.
"We'll see what happens, I think things will move in the market, we will be prepared, we will need to do something knowing the limitations of that market in January and the limitations we have as well to sign players."