In contrast, the visitors sit top of Group E having taken four points from a possible six thus far.
Omonia are plying their trade in the Europa League group stages for the first time in the club's 72-year history, and the Cypriot powerhouses are certainly finding out just how difficult it is to mix with the big boys.
Indeed, Henning Berg's men opened their European campaign with a 1-1 draw away at PAOK before falling to defeat to Dutch giants PSV Eindhoven on matchday two, with Jordi Gomez's opener cancelled out by two Donyell Malen strikes - one of which came right at the death to deny Omonia a point.
Of course, Berg knows what it takes to perform on the big stage following his days with the celebrated Manchester United squad of 1999, but the Norwegian is facing an uphill battle to steer his side to a top-two finish in Group E, with Omonia dropping down to the Europa League after being knocked out by Olympiacos in Champions League qualifying.
Despite finishing top of the pile in last year's abandoned Cypriot first division, 20-time champions Omonia have struggled to assert their dominance this time around and are winless in four across all competitions, with Olympiakos Nicosia getting the better of Berg's men before Omonia take on a Granada side enjoying a far better spell of form by contrast.
As is the case with their midweek hosts, Granada are enjoying their inaugural spell in the Europa League proper this season, with Diego Martinez's men sweeping aside the competition in the qualifying rounds to enter Group E.
The Spanish outfit impressed with a 2-1 victory at PSV on matchday one, but Granada were unable to make it two for two last week as they played out a goalless stalemate with PAOK - a result which keeps them top of the rankings, however.
Granada are certainly not a team associated with evoking fear into the hearts of opponents, but Martinez's men have picked up where they left off last season and have only lost one of their last 12 in all competitions, with the La Liga side looking to stretch their unbeaten run to eight matches when they travel to Cyprus in midweek.
However, the tone was set early in Granada's weekend showdown with Levante; Maxime Gonalons was sent for an early bath after just 16 minutes of the tie - by which point Martinez's side were already 1-0 up courtesy of a Darwin Machis goal - but Levante could only take a point off of the 10 men of Granada as Ruben Vezo levelled before half time.
Omonia Europa League form: DL
Omonia form (all competitions): WWDDLL
Granada Europa League form: WWWWD
Granada form (all competitions): DWWWDD
Despite the hectic fixture schedule taking its toll on teams across Europe, Omonia have no injury or suspension concerns whatsoever for Thursday's bout.
Berg has stuck with the same starting XI for both of Omonia's group stage matches thus far and will be hoping that the third time is the charm here, although Ernest Asante and Giannis Kousoulos will both be vying for starts.
Veteran forward Roberto Soldado has not played a part in either of Granada's group stage matches after testing positive for coronavirus, but the 35-year-old has now completed 14 days of self-isolation and could be involved assuming his PCR comes back negative.
Former Watford man Luis Suarez will be looking to come back into the first XI after occupying a spot on the bench against Levante, with Gonalons available here despite a domestic suspension.
Omonia possible starting lineup:
Fabiano; Hubocan, Luftner, Lang, Lecjaks; Gomez, Gomes; Asante, Papoulis, Tzionis; Duris
Granada possible starting lineup:
Silva; Puertas, Vallejo, Duarte, Neva; Gonalons, Herrera; Soro, Eteki, Machis; Suarez
We say: Omonia 0-2 Granada
Both sides are still finding their feet in European competition as they look to do their countries proud, but Granada are enjoying a much stronger spell of form and will feel confident of taking maximum points from this one. Even with their hefty injury list - which is likely to see Martinez's men line up without a recognised right-back - we are backing the visitors to prevail nonetheless.