The visitors, meanwhile, have only gained one point from their two matches in the competition.
Match preview
For Basel, this is their second successive season competing in the Europa Conference League, having been defeated 4-2 on aggregate by Marseille at the last-16 stage.
After winning eight consecutive Swiss Super League titles between 2009 and 2017, they have fallen off their domestic perch in recent times, having seen Young Boys (four times) and FC Zurich lift the title in the ensuing years.
As such, they have not competed in the Champions League group stage or beyond since, and they may view the Europa Conference League as a more realistic trophy which they can challenge for in any case.
84-time Swiss international Alexander Frei was appointed as head coach during the summer, and while they have fallen eight points behind Young Boys in their domestic table - albeit with one match in hand - their form in a generous Europa Conference League group has been impeccable so far.
As such, should they beat Slovan Bratislava at St Jakob-Park as expected on Thursday, they will move at least six points clear of third spot and take a huge step towards booking their place in the knockout stages.
Slovan Bratislava, on the other hand, are in the midst of the most successful era in their history, having won the Slovakian Fortuna Liga for four successive seasons.
Former Slovakia boss Vladimir Weiss has won two of those titles and looks on course to add a third having taken 26 points from 11 league matches to open up a four point gap at the top of the table.
In Europe, though, they have still failed to progress from the group stage of any competition in the modern era, with their 3-2 win against Barcelona in the 1968-69 Cup Winners' Cup final undoubtedly remaining the most glorious achievement in the club's history.
After finishing third in Group F of this competition last season, Weiss may have his sights set on bagging second spot in the group, having been placed alongside FC Pyunik of Armenia and FK Zalgiris of Lithuania as well as their forthcoming opponets.
Any positive result away to the toughest team in the group upon their trip to Switzerland would represent a bonus, although they will not want to fall too far behind their rivals with games running out.
Basel Europa Conference League form:
L
W
L
W
W
W
Basel form (all competitions):
W
L
W
W
W
W
Slovan Bratislava Europa Conference League form:
L
W
D
L
Slovan Bratislava form (all competitions):
D
L
L
W
D
L
Team News
Basel are likely to be without Riccardo Calafiori, Sergio Lopez, Yannick Marchand, Emmanuel Essiam, Anton Kade and Tician Tushi due to injury on Thursday.
After a closely fought 3-2 win against St Gallen at the weekend, Weiss may look to make a few changes, with Liam Millar, Jean-Kevin Augustin and Adam Szalai likely to receive game time from the start.
Slovan Bratislava, meanwhile, will remain without Michal Sulla due to a long-term cruciate ligament injury, while Jaba Kankava is still suspended after his dismissal in the final qualifying round.
Former Watford midfielder Juraj Kucka is set to start in midfield, while Weiss' son - and namesake - Vladimir Weiss will hope for minutes from the bench.
Basel possible starting lineup:
Hitz; Lang, Freixas, Kasim, Katterbach; Xhaka, Burger; Ndoye, Augustin, Millar; Szalai
Slovan Bratislava possible starting lineup:
Chovan; Kashia, Abena, Morlacchi; Pauschek, Kucka, Agbo, Zmrhal; Barseghyan, Saponjic, Chakvetadze
We say: Basel 2-1 Slovan Bratislava
We expect Basel to claim a hard-fought victory at home on Thursday.
Slovan Bratislava are likely to make life difficult for them given their desire to avoid defeat, but the hosts should have too much quality for them in the end.