Both sides top their respective leagues after making superb starts to the season, with Murat Yakin's Basel having lost just one of their 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 sit third in Group E with four points from three matches, a 2-1 win at UEFA Europa League champions Chelsea in September providing the highlight of their 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 equaliser for the Swiss outfit.
The result extended their unbeaten record on the road to 14 matches and the signs are looking good for Basel, who lead second-placed Grasshopper by two points.
Aiming for their 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 they are to be victorious in this encounter, having failed to win any of their four previous matches on matchday four of the Champions League group stage.
They have won two of their 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 them 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, who sit bottom of Group E with just one point from their three matches, are three points clear in the Romanian top flight.
With nine victories and two draws, they are 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 their 2-0 win over Poli Timisoara last week, a result that saw them qualify for the quarter-finals of the Romanian Cup.
While Steaua look well placed for a 25th Romanian title, they have little Champions League experience, with only midfielder Ionut Neagu and forward Pantelis Kapetanos having played in the competition before this season.
They have not won in four matches in Switzerland and are likely to be without midfielder Mihai Pintilii (muscle strain).
Ella Toone: Why isn't the midfielder playing for Manchester United and England?
'David Beckham was desperate to play in my squad, but I didn't want to bring him along and waste the FA’s money: I had to pick the strongest players': Great Britain coach reflects on Becks snub as 'one of the toughest decisions' of his career
