The Englishman, on loan from Queens Park Rangers, is still serving a 12-match suspension imposed by the Football Association following his conduct against his former club Manchester City on the final day of last season.
That will keep him out of domestic action for OM until at least November 17's clash with Bordeaux, but he is available for European games and has been included in an 18-man squad for the Group C opener against Fenerbahce in Istanbul.
Baup told the club's website: "Every player at the top level is obviously impatient to get into action.
"He has been suspended for a long time and has not been able to do his job. There is, therefore, a strong desire on his part to play in this match."
Baup can also welcome back Loic Remy and Morgan Amalfitano after injury kept them out of Sunday's win over Nancy in Ligue 1.
Defender Nicolas N'koulou is looking forward to experiencing the intense atmosphere of the Sukru Sarakoglu stadium.
"Playing there is special, especially with the atmosphere, and I want to experience that," he said.
"They are a team to take seriously, a big club with a big history. We will do what we can to get something from the game."
Fener's Senegal striker Moussa Sow knows what to expect from Marseille, having played in France - the country of his birth and which he represented at under-21 level - for six years with Rennes, Sedan and Lille.
"First of all, tomorrow's [Thursday's] match will not be easy," he told reporters at a pre-match press conference.
"I think it will be difficult. Marseille have started well in the league this year and won five games in a row."
The 10million euro signing has faced criticism this season after scoring only twice in five games and acknowledged: "I came to Fenerbahce to score goals and that is what they signed me for.
"But a striker is not only there to score goals, but also to play deeper, make key passes and help the team as a whole."
Dirk Kuyt and Mehmet Topal have joined Milos Krasic on Fener's injury list, and there are also doubts over Serdar Kesimal and Egemen Korkmaz.