The 29-year-old, who has 85 international caps to his name, has currently captained Ireland on 38 occasions, leading them to an impressive 28 Test wins since 2002.
"I know Brian better than anybody and he's definitely Lions captain material," said O'Sullivan, who was part of Sir Clive Woodward's Lions coaching set up three years ago.
"He's certainly captain material for Ireland and the Lions. There's no doubt in my mind that here's more than capable of doing the job.
"He was very unfortunate the last time round that, when we came to the business end of the tour, he was injured and didn't really get to captain the Lions in the Test series."