A strict system of testing has so far kept the number of cases in the English top-flight low, even as Britain faces a second wave of COVID-19 infections.
West Ham United boss David Moyes and players Issa Diop and Josh Cullen tested positive this week, while Ilkay Gundogan became the third Manchester City player to return a positive test this month.
But no Premier League game, all taking place behind closed doors, has so far been postponed since last season resumed in June.
Clubs are set to lose their players during next month's international window, which includes European championship and FIFA World Cup qualifiers in South America.
Top clubs reportedly held talks with world governing body FIFA this week over the next two international windows, in October and November.
Concerns are growing that players will be at greater risk of contracting the virus as they criss-cross the globe to represent their countries or being forced into periods of quarantine when they return to their clubs.
Arteta, who tested positive for COVID-19 days before the 2019-2020 season was put on hold in March, said he had his "fingers crossed".
"We have a system that works, that has created a positive, really, really low across the league," the Gunners boss said.
"Obviously when everybody starts to fly away to very different countries I think at the moment is a little bit of an experience and we don't know what the outcome is.
"We want to believe that they want to follow a lot of things that are implemented and are working well so fingers crossed that we don't get any bad news."