The Gunners lost the services of Emiliano Martinez to Aston Villa at the start of the season after the Argentine departed in a £20m move.
That prompted Arteta to bring in Alex Runarsson from Dijon as an understudy to Bernd Leno, who is the undisputed number one at the Emirates Stadium.
Arsenal have sent third choice goalkeeper Matt Macey on loan to Hibernian and Runarsson could be allowed to depart on similar terms after making two mistakes that resulted in a 4-1 defeat to Manchester City in the Carabao Cup last month.
"We are assessing the situation with the three positions on the goalkeeping area and we will find a different solution, probably in this window," Arteta said on Monday.
"We are assessing what is going to happen with the three positions, the discussions we had in the summer within the club are a little bit different to what actually happened because of the transfer window and the situation that developed with Emi.
"We didn't have much time to do what we really wanted to do and we decided to assess the situation in this window, which is what we are trying to do and we will make a decision on how we want to move forward in those three positions."
