The 29-year-old has 85 Ireland caps to his name and is the current Ireland captain after leading them in 38 matches. Under his captaincy Ireland have won 28 times 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 in New Zealand.
"He's certainly captain material for Ireland and the Lions. There's no doubt in my mind that he's more than capable of doing the job." he said.
"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."