Having impressed in a group featuring Real Madrid and Inter Milan last term, their ambitions have been renewed under new management, while the hosts missed out on Europe entirely last year and are keen to rejoin the elite.
Appointed Shakhtar Donetsk coach in the summer after a successful three-year spell at Sassuolo, the charismatic Roberto De Zerbi penned a two-year contract with the wandering Ukrainian club.
Having coached Italy stars Domenico Berardi, Manuel Locatelli and Giacomo Raspadori while at the Mapei Stadium - a talented trio that were part of the Azzurri's Euros win this summer - he is no stranger to managing players with great individual quality. Now, he leads his new team into the qualification process for a place at Europe's top table.
Since 2014, Shakhtar have been based in Lviv, then between Kharkiv and Kiev, as the Donbass region remains embroiled in a territorial dispute with neighbouring Russia. Despite such turmoil, the Miners have still enjoyed success on the continent - beating Real Madrid home and away last year, but being eliminated at the Champions League group stage - after a run to the semis of the 2019-20 Europa League just a few months before.
However, they let their four-year grip on the title slip in the spring, seeing rivals Dynamo Kiev pip them to the league crown and an automatic berth in the Champions League group phase. Following the subsequent departure of Portuguese coach Luis Castro, the highly-rated De Zerbi stepped in, and his debut in the Ukrainian top flight brought a dominant home win against Inhulets last week.
Though the game ended 2-1, first-half goals from new signing Lassina Traore and midfield stalwart Alan Patrick saw Shakhtar control affairs, before they went on to claim maximum points from their first two fixtures with a 3-0 victory over Lviv on Saturday. Traore was on target again, as they rattled in three unanswered goals in the final 20 minutes - serving as the ideal warm-up for this week's trip to Genk.
Their hosts on Tuesday, meanwhile, were held to a 1-1 draw away to Standard Liege on the opening day of the Belgian Pro League season, before hosting Oostende on Friday evening; welcoming fans back to their Luminus Arena home in the process.
Following a tradition of playing front-foot football, Genk were the league's top scorers last term - Nigeria international Paul Onuachu leading the way with 35 goals in all competitions - and they certainly lived up to that reputation in a frantic 4-3 defeat.
Having lead both 2-0 and 3-2 before a late collapse, manager John van den Brom expressed his frustration after the game and - following on the heels of a Super Cup defeat to Club Brugge last month - the Blauw-Wit have hardly made an ideal start to the new campaign.
Onuachu, in particular, has faced criticism for his under-par displays and less heralded countryman Cyriel Dessers has been preferred of late, despite Van den Brom's pleas for patience with his star striker. Since the 1979-80 season, no one has scored more in a Belgian season than the giant forward managed in 2020-21, but interest from West Ham United has apparently fizzled out and his form has waned.
After his current club made the Champions League group stage for only the second time in 2019-20 - finishing fourth in a section also featuring Liverpool, RB Salzburg and Napoli - Genk will now be determined to return after a year out of Europe entirely, but will be up against it versus an experienced Shakhtar side.
As expected, new Shakhtar coach Roberto De Zerbi has so far deployed his preferred 4-2-3-1 formation - prioritising possession and an attacking philosophy which will surely suit his technically adept playing staff.
The latest Brazilian to join a growing South American enclave is centre-back Marlon, who followed his boss from Sassuolo this summer, and he should start at the heart of the visitors' back four in Belgium. Serhiy Kryvtsov remains doubtful due to a knee injury, though, so Mykola Matviyenko will be his partner.
Though Chelsea youngster Ike Ugbo has apparently agreed personal terms with Genk - after scoring 17 times on loan at Cercle Brugge last season - his move has yet to be confirmed, so either Paul Onuachu or Cyriel Dessers will start in attack for the home side.
Another member of the Genk forward line, Japanese winger Junya Ito, poses a danger on the right; regularly getting into shooting positions and combining well with the frontman.
The hosts can now benefit from the inclusion of their Copa America players - Colombia's Daniel Munoz and Carlos Cuesta, plus Angelo Preciado of Ecuador - who recently rejoined the squad, while Kristian Thorstvedt overcame a knee problem to feature from the bench at the weekend and should be available once more.
Genk possible starting lineup:
Vandevoort; Preciado, Sadick, McKenzie, Arteaga; Heynen, Hrsovosky; Ito, Tresor, Bongonda; Onuachu
Shakhtar Donetsk possible starting lineup:
Trubin; Dodo, Marlon, Matvienko, Kornienko; Maycon, Stepanenko; Pedrinho, Patrick, Solomon; Traore
We say: Genk 1-2 Shakhtar Donetsk
The combination of numerous years worth of European experience and an exciting new regime in the dugout should take Shakhtar to a first-leg lead on Tuesday, in a game that could flow end to end.
Genk's slow start to the season has already put them on the back foot, so if they can stay within a goal of their Ukrainian counterparts ahead of next week's second leg, that may not be the worst of results.