Leverkusen ran out 4-2 winners in Israel in the recent meeting between the two sides.
With two wins and a loss from their opening three matches in Group C, Peter Bosz's side are in a strong position to progress to the knockout stages of the Europa League for the third successive season.
Bosz most likely does not expect to be in this competition next season, however, with qualification for the Champions League via a league position - or winning the Europa League - a very realistic aim for his side this season having narrowly missed out last time around.
Indeed, Saturday's late 2-1 win at Arminia Bielefeld saw them rise to third in the Bundesliga table, level on points with Borussia Dortmund and just a point behind leaders Bayern Munich after eight matches.
A win against Be'er Sheva on Thursday would take them six points ahead of their opponents with only two games remaining, with the amount of overall breathing space they would have dictated by the outcome between Nice and Slavia Prague in the other match in the group.
Yossi Abukasis will have taken some encouragement from his side's 4-2 defeat to Leverkusen in the last meeting between the two sides, with Elton Acolatse's first-half brace giving the Israeli outfit a surprise lead before the Germans struck back.
Be'er Sheva have not generally been proficient travellers in this competition in recent years, though, winning only two of their 16 away matches. One of those was a famous 2-0 win at Inter Milan in 2016, though, so Abukasis will be calling on his players to do the unthinkable once more when heading to Leverkusen.
A defeat could see them facing an incredibly uphill task to qualify for the knockout stages, particularly if Slavia Prague beat Nice in the other match in the group, as this would leave the Israeli side six points behind both Leverkusen and Slavia Prague with only two matches remaining.
They will certainly need to improve on their recent league form if they are to have any chance of gaining a result, having only taken six points from six matches in the Israeli Premier League so far this season.
Bayer Leverkusen Europa League form: WLW
Bayer Leverkusen form (all competitions): WLWWWW
Hapoel Be'er Sheva Europa League form: WLL
Hapoel Be'er Sheva form (all competitions): DLDLDL
Bosz is missing several players for the match against Be'er Sheva, with Edmond Tapsoba (coronavirus), Exequiel Palacios (back), Charles Aranguiz (muscular), Paulinho (knee) and Santiago Arias (fibula) all ruled out of the fixture.
Patrik Schick made his return to action from the bench in the win over Arminia at the weekend, having not featured since early October after tearing a muscle. He may start in order to gain crucial match fitness.
Acolatse did not feature in the weekend defeat at Ashdod, but should return to the side having scored a brace in the last meeting between the sides.
Bayer Leverkusen possible starting lineup:
Hradecky; Jedvaj, Tah, Dragovic, Wendell; Demirbay, Baumgartlinger; Bellarabi, Wirtz, Bailey; Schick
Hapoel Be'er Sheva possible starting lineup:
Levita; Taha, Tzedek, Kabha; Dadya, Josue, Bareiro, Goldberg; Sallallich, Agudelo, Acolatse
We say: Bayer Leverkusen 3-0 Hapoel Be'er Sheva
We expect Leverkusen to have far too much class for the visitors to handle, even with a raft of changes likely to be made by Bosz.
Providing he is fit enough to start, Schick will be motivated to make a huge impact on his return to first-team action.