The Swiss hosts and the Romanian visitors sit third and fourth in the table and are looking for three points to revitalize their European efforts.
Both sides top their respective leagues after making superb starts to the season, with Murat Yakin's Basel having lost just one of its last 16 matches in all competitions.
That defeat came in the Champions League as Julian Draxler's second-half strike helped Schalke to a 1-0 win last month.
Basel sits third in Group E with four points from three matches, a 2-1 win at Europa League champions Chelsea in September providing the highlight of its campaign.
The hosts will enter the match on the back of a 1-1 draw at struggling Aarau on Saturday, with Marco Streller scoring a 93rd-minute equalizer for the Swiss outfit.
The result extended its unbeaten record on the road to 14 matches and the signs are looking good for Basel, which leads second-placed Grasshopper by two points.
Aiming for its fifth successive Swiss Super League title, the goals of Streller have been important.
The 32-year-old has netted seven in 11 league matches, while he also scored in the win over Chelsea.
Basel will have to reverse history if it is to be victorious in this encounter, having failed to win any of its four previous games on matchday four of the competition's group stage.
The club has won two of its home matches against Romanian sides in the Champions League and claimed a 1-1 draw at Steaua last month.
Steaua needed a Leandro Tatu strike with just two minutes to play to give it a point, and Basel will be determined to grab revenge.
Midfielder Valentin Stocker (groin) is a doubt after missing Saturday's draw, while defender Behrang Safari (thigh) will definitely miss.
Steaua, which sits at the bottom of Group E with just one point from its three matches, is three points clear in the Romanian top flight.
With nine victories and two draws, it is yet to taste defeat, and Italian striker Federico Piovaccari has been in terrific form, scoring five times in seven league matches.
Piovaccari also netted in the 2-0 win over Poli Timisoara last week, a result that saw Steaua qualify for the quarterfinals of the Romanian Cup.
While Steaua look well placed for a 25th Romanian title, it has little Champions League experience, with only midfielder Ionut Neagu and forward Pantelis Kapetanos having played in the competition before this season.
The club has not won in four matches in Switzerland and is likely to be without midfielder Mihai Pintilii (muscle strain).