O'Driscoll and O'Connell played key roles in Ireland's Grand Slam victory
Former British and Irish Lions skipper Gavin Hastings thinks the captaincy for the South Africa tour is between Brian O'Driscoll and Paul O'Connell.
Head coach Ian McGeechan will name his Lions squad next month ahead of the 10-week trip to South Africa.
And Hastings has tipped O'Driscoll to pip his Irish team-mate after leading Ireland to the Grand Slam on Saturday.
"Undoubtedly it's going to be between Brian and Paul, but Brian has to be the favourite," the Scot told BBC 5 Live.
"Paul O'Connell is a wonderful leader of the team as well, but Brian has just lifted Ireland's first Grand Slam in 61 years.
"In this day and age of rugby there are normally four or five leaders on the field and that will continue with the Lions.
"I just think Brian O'Driscoll has played so well this year it would almost be a fitting tribute to the way he has played were he to be named Lions skipper."
But three-times Lions tourist and former England back-row Richard Hill believes the Munster lock should get the nod ahead of the Ireland captain.
"I would go for Paul O'Connell," Hill told BBC Sport. "He is a good man, he is well respected, he trains very hard, he's very much a man to gain inspiration from and is a leader on the pitch."
Hill, who was part of the successful 1997 tour to South Africa but was injured while in Australia in 2001 and again in New Zealand four years later, thinks there may yet be a surprise nomination.
"There are equally good candidates out there at international level. Obviously for Ireland Paul is captained by Brian, who was great in the early stages of the New Zealand tour before his injury in the first Test.
"There are a number of candidates who you'd have no qualms about leading the British and Irish Lions and there are probably even a few candidates who don't lead their international sides who could also do a good job," Hill added.
There haven't been many successful Lions captains from outside the scrum
Former England and Lions centre David Duckham
David Duckham, the former England centre and Lions tourist of 1971, told BBC Sport he thinks there is a case for picking a forward as the Lions skipper.
"O'Driscoll could definitely be the captain but maybe outside centre is not the best position to captain a Lions team from.
"I would err on the side of a forward being captain, ideally in the back row where you can see what's going on in the game.
"There haven't been many successful Lions captains from outside the scrum; there was John Dawes in my day at centre, but look at Willie John McBride and, of course, Martin Johnson."
Hastings led the Lions on their 1993 tour of New Zealand, narrowly losing the three-Test series 2-1.
McGeechan was a coach on that tour, and Hastings believes the Wasps coach will select more England players in his squad than many predicted before their victories over France and Scotland to complete their Six Nations campaign.
"There's no doubt the majority of players will come from Wales and Ireland, but England's strong finish to the Six Nations, pushing them up to second, means they will feature a lot of players," the former Scotland full-back told 5 Live Sport.
"All credit to them for coming good. You sensed the influence of (coach) Martin Johnson was slowly beginning to come through."