Iceland international Runarsson, 25, underwent a medical in France yesterday ahead of travelling to the capital to wrap up his switch.
Manager Mikel Arteta said: "Obviously with the departure of Emi which is a big loss and someone that I think we always want the best for what he has done for the football club and also the person he is, we have to replace him and we have been looking in the market and I think that we will shortly be in a position to announce our new signing.
"I don't know [if it will be announced in hours or days]. In football the hours can become days and something that looks unlikely can happen straight away so unfortunately I cannot tell you."
Arteta said: "Depending on what is going to happen with our third goalkeeping position as well because we have some talks about that in the last few months. But still the market is open and things can change."