Tierney and Celtic midfielder Ryan Christie were asked to quarantine for 14 days after their Scotland teammate Stuart Armstrong tested positive for coronavirus while the trio were on international duty.
Although both Tierney and Christie have repeatedly returned negative test results for the virus, the Lothian Health Protection Team identified the pair and two members of Scotland's backroom staff as close contacts of Armstrong.
"This is getting very complicated when we are sending players abroad and obviously you lose control and some authorities have different regulations to the ones in the Premier League," Arteta said at a news conference on Thursday. "We are still having some discussions with the authorities and hopefully we will know more this afternoon."
Asked whether there was a chance Tierney could play, Arteta added: "I hope so."
Arsenal have lobbied the Scottish government to release Tierney, submitting photographic evidence that shows he was sitting further away than the socially distancing requirement of two metres when playing computer games in a hotel room with Armstrong and Tierney.
The international break has caused a variety of logistical issues relating to coronavirus for many clubs but Arteta is not in favour of scrapping next month's matches.
"I think international football has to continue going because there are some competitions that have to happen," Arteta said. "They were already delayed last summer and they have to take place because as well those organisations have to be sustainable and we all understand that.
"What we are asking is that we try to unify those protocols, rules to try to create a safe environment for our players, but as well protect the clubs because obviously the impact of having a few players out when we resume the Premier League is really big."