The Ireland centre suffered a back spasm during the RaboDirect PRO12 play-off victory over Glasgow last weekend.
He did not attend Monday's initial British and Irish Lions squad gathering in London, but Leinster say O'Driscoll is currently rated as having "a good chance" of being available for the final.
O'Driscoll is among six Leinster players - Rob Kearney, Jonathan Sexton, Cian Healy, Sean O'Brien and Jamie Heaslip - selected for the Lions tour to Hong Kong and Australia.
Flanker O'Brien is expected to face Stade Francais after he missed the Glasgow encounter due to a calf muscle injury, but centre Gordon D'Arcy has been ruled out of the final due to calf trouble.
Leo Cullen, Kevin McLaughlin, Fergus McFadden and Richardt Strauss, meanwhile, are recovering from a variety of bumps and bruises but should all be in contention.
- Sports & Recreation
- Cian Healy