The Scotland left-back is currently in 14-day isolation after his international teammate, Stuart Armstrong, tested positive for coronavirus.
Tierney has repeatedly tested negative for the virus and maintains that he kept his distance from Armstrong.
Arsenal have argued with the Lothian health authorities to release Tierney, and Arteta hasn't given up hope yet.
Asked if Tierney will be available, Arteta said: "I hope so.
"This is getting very complicated when you are sending players abroad and obviously you lose control.
"Some authorities have different regulations to the actual ones in the Premier League. We are still having some discussions with the authorities and hopefully we will know more this afternoon."