HSBC ambassador Hastings said: "You have to pick someone who is respected by his peers and who is likely to have a regular starting berth in the team and, for me, Brian is that man."
Hastings, capped 61 times by Scotland and a veteran of two Lions touring teams, also believes that O'Driscoll is showing signs of regaining the form that has seen him tour twice with the Lions in 2001 and 2005.
"You need to pick players who are in form, and following his performance for Leinster (against Edinburgh) at the weekend, if you were to ask me to pick a captain now, it would be Brian O'Driscoll.
"If the Lions are to be successful this time around, you need players with strength of character and guys to lay down the law.
"If you look back at the last successful Lions tour in 1997, coaches like Jim Telfer and players such as Keith Wood were excellent at laying down what was required.
"It's all about getting the best from the players and Brian would be a fantastic man to do that," he added.
Hastings also believes the key to a Lions series victory would be to learn lessons from the mistakes made last time around and insists coach Ian McGeechan is the right man for the job.
"Finding a blend is absolutely key. You are trying to put 15 guys together who haven't played together ever, starting afresh and asking them to perform with all the history and tradition," he explained.
"Sir Clive Woodward took too many players in 2005 to form any kind of unit but Ian McGeechan is too shrewd and too steeped in Lions history to make the same mistake.
"You look at the guys who played in the successful 1997 tour, such as Tom Smith, Jeremy Davidson, Keith Wood, they bonded as a team and that made all the difference.
"'Geech' is sure to repeat that trick this time around and will certainly pick those who are performing at the right time, and not those with the reputations - for me, that's the key."