O'Driscoll's calf tightened up in training on Tuesday morning and a clearer picture of the severity of the problem will emerge over the next two days.
Leinster's Luke Fitzgerald has remained with the senior squad to cover for the Ireland centre in case his condition deteriorates.
But O'Sullivan is convinced his skipper will be available for the Croke Park showdown against Frank Hadden's Six Nations strugglers.
"We expect Brian will be fine but as a precaution I'm holding onto Luke Fitzgerald, who would have been playing for the A team," he said. "When a player gets a niggle early in the week it's a concern, but it's only Tuesday and the match is Saturday, so I'm confident he'll be fine.
"However, it's Six Nations rugby and you have to cover the doomsday scenario in case Brian doesn't make it. Having Luke there is just a precaution and I'm not worried. We'll be better equipped to make a judgment tomorrow and the day after.
"Brian is a power runner and he does pick up the odd tweak, but the doctor is very confident."
Should O'Driscoll be forced out against the Scots, Shane Horgan will be promoted from the bench to centre with Fitzgerald plugging the gap among the substitutes.
As it stands, Horgan must watch from the sidelines for the second successive Six Nations match after Tommy Bowe was catapulted straight into the starting line-up.
The clamour for Bowe's inclusion, which has gathered momentum on the back of his dazzling form for Ulster this season, could no longer be ignored by O'Sullivan.
The Ospreys-bound 23-year-old won his 10th cap in last August's World Cup warm-up against Scotland but lost out on selection for the tournament to Brian Carney.
Andrew Trimble, Geordan Murphy and Rob Kearney have since been preferred in the Six Nations to date but Murphy's fragile display against France has opened the door.
"Tommy is playing really well and has forced his way into the team," said O'Sullivan. "Geordan has sustained a knee injury. It's a nasty knock he suffered on Sunday while playing for Leicester.
"He would have been very doubtful for Scotland but to be up front about it, he would not have made the 22 anyway. Geordan had a difficult match against France. You have to weigh that up against someone like Tommy, who has really been putting his hand up."