The Gunners will be among the seeded clubs in the non-champions section, and so cannot face the likes of AC Milan, Schalke or Lyon. But they could face Fenerbahce or Ukrainians Metalist Kharkiv - though the participation of both these teams in the competition proper could yet be in doubt because of legal disputes.
The prospect of a trip to Turkey or Ukraine will be one manager Arsene Wenger wants to avoid most, especially if the second leg proves to be away in the same week as they host north London rivals Tottenham.
Arsenal have yet to make any major signings this summer and appear unlikely to do so before Monday's deadline to feature in the two legs - the first of which will come just a few days after the start of the new Barclays Premier League campaign.
Real Sociedad, who finished fourth in La Liga, boast former Gunner Carlos Vela in their ranks and have spent some of their pre-season in England, drawing 1-1 at Norwich in midweek ahead of a friendly meeting with Southampton.
PSV Eindhoven finished second in the last Dutch championship and would represent a more favourable opposition, as would Portuguese side Pacos de Ferreira, who have never qualified for the Champions League.
Arsenal, though, have some pedigree in reaching the group stages via an all-or-nothing tie, as they battled past Udinese two seasons ago and swept aside the challenge of Celtic ahead of the 2009-2010 campaign.
Nevertheless, Wenger will take nothing for granted and has no intention to leave anything to chance having fought so hard for the right to play among Europe's elite clubs once again.
He said: "Our immediate aim is to start well in the Premier League and to qualify for the Champions League group stage.
"That is always a huge challenge, which demands a lot of energy, but we fought hard to be in this position last year, so we want to take the next step now."