Both clubs overcame shocks in their second legs to earn their places in Friday's last-16 draw, with Dortmund scoring a late equaliser against Atalanta to advance on a 4-3 aggregate score.
Arsenal held a 3-0 lead from their first leg with Ostersunds, but two first-half goals from the visitors put Arsene Wenger's side under pressure before Sead Kolasinac sealed their progression.
The Gunners broke their club transfer record to sign Pierre-Emerick Aubamayeng from the German side during the January transfer window, and Stoger is hoping that the two clubs will not meet in the next round of the Europa League.
It would be the first time since the 2014-15 Champions League group stage for the pair to meet, with both clubs recording 2-0 wins in their home grounds that season.
In the early part of the decade, the sides seemed to be constantly drawn against each other, facing off in the 2011-12 and 2013-14 Champions League group stage as well as in 2014-15.
Stoger believes it would be interesting to face the Gunners again, but would prefer a different name to be drawn from the pot, telling Sport1, it would be "curious and funny, but there are certainly other clubs that we would rather have now."
The Europa League last-16 draw takes place on Friday, February 23 at 12:00 GMT and is being held at UEFA's headquarters in Nyon. It is an open draw with no seeding, meaning any of the 16 teams could face each other.