The Swedish side lifted European football's second-tier trophy back in 1982 and again in 1987 under its former guise of the UEFA Cup, but their ambitions for this year's tournament are likely to be much smaller as they approach the first leg of their second-qualifying-round clash in Hungary.
Mikael Stahre's men were third in the Allsvenskan last season, but currently sit a disappointing sixth after 14 games this term and will likely need to improve after only defeating Luxembourg's Fola Esch 2-0 on aggregate in the previous round.
Gothenburg will not be the only Swedish team aiming to try and seal a place in the third qualifying round, with Elfsborg, AIK and Brommapojkarna taking on Inter Baku, Linfield and Crusaders respectively.
Rosenborg were surprisingly eliminated at the same stage last season, losing out to Scottish side St Johnstone, and they will hope to avoid a repeat against Ireland's Sligo Rovers.
Swiss side Luzern are the opponents on this occasion for St Johnstone, who are one of three Scottish teams competing in the Europa League.
Motherwell meet Icelandic side Stjarnan, while Aberdeen face a tricky test against Eredivisie play-off winners Groningen in what should be one of the standout ties of the round.
Norwegian's Tromso were the big winners of the first qualifying round, hammering Tartu Santos of Estonia 13-1, and they will be looking for more of the same against Faroese outfit Vikingur.
Tippeligaen leaders Molde meet Gorica of Slovenia, while Norwegian compatriots Haugesund will need to overcome Sarajevo.
Zulte-Waregem and Shakhter Karagandy take on Zawisza Bydgoszcz and Atlantas respectively as they both aim to feature in the group stage for a second straight year.
Lech Poznan, last-32 participants in 2011, will be favourites against Estonia's Nomme Kalju, and their Polish compatriots Ruch Chorzow should be hopeful of progress against Vaduz of Liechtenstein.
Romanian's Cluj make their return to European football after a year-long absence against Jagodina, while Petrolul Ploiesti face Flamurtari Vlore as they bid to go better than last season's run to the final play-off round.
Zimbru will require a fine performance in order to knock-out CSKA Sofia of Bulgaria, and Chikhura are also likely to be up against it in their tie with Bursaspor.
Kazakhstani sides Astana and Kairat meet Hapoel Tel Aviv and Esbjerg, the latter of whom reached the last 32 in 2013-14.
Finnish teams RoPS and MYPA are pitted against Asteras Tripolis and Dinamo Misnk, whose fellow Belarusians Neman Grodno and Shakhtyor will need to overcome FH and Derry City.
Kosice face Slovan Liberec, Laci meet Zorya and Neftci take on Koper, while the games between Omonia Nicosia and Buducnost, Vojvodina and Trencin, Zestafoni and Spartak Trnava and St Polten and Botev Plovidiv should all be hotly contested.
Meanwhile, Sillamae Kalev host Krasnodar, Rijeka welcome Ferencvaros, Hajduk Split travel to Dundalk and the Croatian side's city rivals RNK Split meet Hapoel Be'er Sheva of Israel.
Elsewhere, there are clashes between Siroki Brijeg and Mlada Boleslav, Diosgyor and Litex Lovech, Metalurg Skopje and Zeljeznicar, while Cukaricki host Grodig.
Get the best features, fun and footballing frolics straight to your inbox every week.
Thank you for signing up to Four Four Two. You will receive a verification email shortly.
There was a problem. Please refresh the page and try again.