Avoiding defeat by four or more goals, meanwhile, will be enough to confirm Leverkusen's qualification for the next round.
Indeed, it has been an extremely disappointing campaign for Patrick Vieira's side so far, losing their last four games in all competitions to slide to 11th in Ligue 1 and all but exit the Europa League.
Sitting six points behind Slavia Prague and their forthcoming opponents with only two matches remaining in Group C, the head-to-head ruling which separates sides level on points means that Nice will need to beat Leverkusen by four or more goals to remain in the competition after losing 6-2 to them earlier in the campaign.
It is not possible for Nice to finish ahead of Slavia Prague having lost both matches to them, including a dismal 3-1 home defeat last week, so Vieira will be hoping the Czech Republic outfit beat Hapoel Be'er Sheva and Leverkusen in their last two matches to help their unlikely cause.
Either way, though, beating a Leverkusen side who are unbeaten after nine matches in the Bundesliga by a margin of four or more goals seems an incredibly tall order.
Indeed, Peter Bosz's side have had an excellent start to the campaign, winning five of their last six matches in the Bundesliga and retaining their unbeaten domestic record to move up to third in the table.
The 1-0 loss at Slavia Prague, when Karim Bellarabi was sent off after only 22 minutes, is the only real blemish on Leverkusen's copybook this campaign, with qualification to the knockout stages of the Europa League all but secured with last week's 4-1 win over Israeli side Be'er Sheva.
Bosz will of course look to win at Nice to boost his side's chances of topping Group C, but even a narrow defeat would ensure Leverkusen's safe passage to the next round, so it is unlikely they will be quite as expansive as normal.
Nice Europa League form: LWLL
Nice form (all competitions): WWLLLL
Bayer Leverkusen Europa League form: WLWW
Bayer Leverkusen form (all competitions): WWWWWD
Hicham Boudaoui is also suspended after his injury-time sending-off in the home defeat to Slavia Prague, with former Southampton and Tottenham Hotspur midfielder Morgan Schneiderlin likely to continue in midfield.
Bosz, meanwhile, is missing a host of players through injury, with Paulinho (knee), Santiago Arias (fibula), Sven Bender (ankle), Edmond Tapsoba (coronavirus), Exequiel Palacios (back), and Charles Aranguiz (muscular) unable to make the trip to Nice.
Top goalscorer Alario missed the weekend's 0-0 draw with Hertha Berlin due to a minor injury, but should be fit to return to what may otherwise be a weakened side.
Nice possible starting lineup:
Benitez; Lotomba, Robson, Nsoki, Pelmard; Reine-Adelaide, Schneiderlin, Maurice; Lopes, Gouiri, Maolida
Bayer Leverkusen possible starting lineup:
Hradecky; Dragovic, Tah, Jedvaj; Bellarabi, Wendell, Demirbay, Wirtz, Amiri; Alario, Bailey
We say: Nice 2-1 Bayer Leverkusen
With Leverkusen facing something of an injury crisis and all but assured of qualification to the knockout stages, we can see Bosz resting as many players as he is able to on Thursday.
As such, Nice should get the win they are looking for, but not by the margin they need to remain in the competition.