The young midfielder is closing on a temporary move to the Gunners lasting until the end of the season after finding chances hard to come by at Real Madrid.
Arsenal have been in the market for a playmaker and moved quickly to beat Real Sociedad to the 22-year-old's signature.
"I think we are pretty close, but it is not finalised," Arteta told reporters after Arsenal's win at Southampton.
"As I am standing here I have not talked to Edu or the club in the last three hours, but we are very positive that we can finalise the deal."
Odegaard has undergone a medical and, should there be no last-minute hitches, will be confirmed as an Arsenal player this week.
Much like Dani Ceballos’s two loan agreements from Real Madrid, Arsenal hold no option to make the move permanent.