Odegaard is keen to leave during the January window to gain more minutes but Arteta would not be drawn on whether he could end up in north London.
"I cannot comment about players that play for different clubs," he said.
Arteta admitted he is looking for reinforcements but said this unique period made the club "cautious" and "careful" in their transfer business.
"We are looking at various positions because the movement we made in this transfer window with some players leaving the club leaves us a little bit short in certain areas. If we can we will do it, if we can't, we'll just keep going with what we have," he said.