The visitors, meanwhile, are seeking to avoid a third successive defeat across all competitions.
Match preview
Just over two-and-a-half years after losing 4-0 over two legs to Manchester United in the knockout rounds of the Europa League, Real Sociedad got their revenge with a slender 1-0 win at Old Trafford in their opening group game last week.
Lisandro Martinez was penalised for a handball inside the penalty area following a strike from former Manchester City star David Silva, with Brais Mendez converting from 12 yards just before the hour mark to seal all three points.
Imanol Alguacil's side were unable to build on their midweek victory, however, as they suffered a 2-1 La Liga defeat away at Getafe last Sunday. Mendez was on the scoresheet again - his third goal in four games across all competitions - but the Erreala were eventually condemned to their second top-flight defeat of the campaign.
Most teams would welcome the return to home soil, but Real Sociedad have struggled in recent Europa League games at the Estadio Anoeta as they have won only two of their last 10 on their own turf.
Sociedad have never faced Cypriot opposition in a competitive match before, but they will be confident of seeing off Omonia on Thursday and maintaining their 100% start in Group E.
Unlike Real Sociedad, Omonia were unable to make a winning start to their Europa League campaign as they suffered a 3-0 home defeat to Sheriff Tiraspol last week.
Nicknamed 'The Queen', the Cypriot outfit have now failed to win any of their seven away matches in European competition, having previously drawn three and lost three over the last two years.
Last season's Cypriot Cup winners, who are managed by former Celtic boss Neil Lennon, have since suffered a 2-1 away loss at Apollon Limassol last Sunday, a result which has seen them slip six points behind the top of the First Division, albeit after only three matches.
Omonia will now turn their attention to Thursday's contest where they will face Spanish opposition for the first time since losing home and away to Granada in the Europa League group stage two years ago.
Real Sociedad Europa League form:
Real Sociedad form (all competitions):
Omonia Europa League form:
Omonia form (all competitions):
Team News
Real Sociedad striker Umar Sadiq is the latest name to join their growing list of injuries and he could face up to a month on the sidelines after twisting his right knee in last weekend's defeat to Getafe.
Mikel Oyarzabal (ACL), Martin Merquelanz (knee) and Carlos Fernandez (hamstring) are also sidelined with injuries while Robin Le Normand (knock) and Diego Rico (hamstring) are both doubtful.
Eighteen-year-old Mohamed-Ali Cho is the most likely candidate to replace Sadiq and join Alexander Sorloth in attack, while Mendez and Silva could be recalled at the expense of Benat Turrientes and Takefusa Kubo respectively.
As for Omonia, new recruit Gary Hooper was an unused substitute over the weekend but he could make his debut on Thursday and join Bruno Felipe in attack.
Lennon is set to stick with a 3-5-2 formation, with Nemanja Miletic, Adam Lang and Nikolas Panayiotou the most likely trio to start at centre-back, while Adam Matthews and captain Jan Lecjaks could continue as wing-backs.
Real Sociedad possible starting lineup:
Remiro; Gorosabel, Elustondo, Pacheco, Munoz; Mendez, Zubimendi, Merino; D. Silva; Cho, Sorloth
Omonia possible starting lineup:
Fabiano; Miletic, Lang, Panayiotou; Matthews, Diskerud, Cassama, Charalambous, Lecjaks; Hooper, Felipe
We say: Real Sociedad 3-0 Omonia
Despite the absence of Sadiq, Real Sociedad still have plenty of quality in the final third and they should have no problems in breaching Omonia's backline.