The eastern European outfit will have to be on top form against the Swiss side, who have beaten Chelsea at Stamford Bridge but slipped to defeat to Schalke last time out
The Romanian champions have faced Chelsea and Schalke so far this season in Group E and were defeated in both games, conceding a total of seven goals and scoring none in the process.
Steaua will no doubt hope to take their domestic form into the Champions League after winning eight and drawing one of their first nine matches of the campaign to set the pace at the top of the table.
A 4-0 away victory at Viitorul Constanta on Friday proved to be the perfect preparation for the visit of Basel.
The form of Italian attacker Federico Piovaccari has played a significant part in the side's successful start to the season as he has scored five goals in seven league appearances, but Basel head to Bucharest in a confident mood themselves.
Murat Yakin's side are also sitting at the top of their own domestic league with 25 points from 12 games and their away form has been a particular highlight in recent weeks.
The Swiss champions have played 11 matches in all competitions on the road and are yet to lose, with their last five away fixtures ending in victory.
Basel's start to this season's Champions League, though, has been mixed. A 2-1 victory at Chelsea on matchday one was the first time they have won a competitive match in England, but their good work was undone by 1-0 defeat against Schalke last time out.
The match will be remembered more for a Greenpeace protest against Champions League and Schalke sponsors Gazprom, but the Germans left Switzerland with all three points thanks to Julian Draxler's second-half strike.
Yakin will be able to rely upon a full-strength squad for the trip. Giovanni Sio is serving a domestic suspension, but he is free to play in Europe, while Marcelo Diaz will be available after returning late from international duty.