Should O'Driscoll fail to recover, Felipe Contepomi will start with Fergus McFadden coming onto the replacements bench.
In the pack, Malcolm O'Kelly continues his second row partnership with Devin Toner, who was the Heineken man-of-the-match in the 33-3 victory over Castres at the RDS last Saturday.
Shane Jennings returns from injury to don the number 7 jersey and the fit-again Isa Nacewa has also been named on the bench.
Several hundred Leinster supporters are expected to make the trip to France for the game.
If O'Driscoll plays in the return match against Castres, he stands a chance of joining the small band of players who have scored 25 tries in the Heineken Cup.
He crossed for his 24th Heineken Cup try in last weekend's victory over Castres.
It was the Ireland captain's fourth try in this season's competition, while his overall try tally has come in 54 matches.
O'Driscoll's Leinster team-mate Shane Horgan is also one try short of the 25-try mark.
Only two players have so far scored 25 Heineken Cup tries or more - Dafydd James (29) and Vincent Clerc (27).
Previewing Friday's encounter, Leinster technical consultant coach Alan Gaffney said: "Castres will be playing with a different team this week, though we have done analysis on them for the last five or six games before this already.
"So we're pretty much aware of the abilities of each of the players without them announcing their team.
"The two nines play differently and we understand that. So we've got to adopt and adapt to the side that they pick.
"There's no doubt that we probably played the game a bit narrow at the weekend. And I think we have been guilty of that. That's something that we have addressed again.
"We have got the ability, we train and we know what we want to achieve. Sometimes we're not backing ourselves to do things, but sometimes we have to set up certain plays and patterns.
"Traditionally speaking, every play we play is one we want to have as a strike play. We put a few things together (in the last game) that we were happy with, but not enough."
LEINSTER (v Castres Olympique): Girvan Dempsey; Simon Keogh, Brian O'Driscoll*, Luke Fitzgerald, Rob Kearney; Jonathan Sexton, Chris Whitaker (capt); Stan Wright, Bernard Jackman, CJ Van Der Linde, Devin Toner, Malcolm O'Kelly, Rocky Elsom, Shane Jennings, Jamie Heaslip.
Replacements: Brian Blaney, Cian Healy, Trevor Hogan, Sean O'Brien, Chris Keane, Felipe Contepomi/Fergus McFadden, Isa Nacewa.