O'Driscoll and O'Connell are thought to be the front-runners for the captaincy
Lions coach Ian McGeechan insists there are "still three or four names" in the frame to lead the squad on their tour of South Africa this summer.
Most pundits believe it is a straight choice between Ireland duo Brian O'Driscoll and Paul O'Connell.
"The captain has got to have a strong character, the respect of others and be able to pull things together quickly.
"He's got to give off the right tone, and be able to deal with tricky situations," McGeechan said.
Wales skipper Ryan Jones, England prop Phil Vickery, who McGeechan knows well as Wasps director of rugby, and Scotland captain Mike Blair could also come into contention.
McGeechan, who met with his fellow Lions coaches on Thursday to review selection after the Six Nations, insists there are still places up for grabs before he names his 35 or 36-man squad on 21 April.
It is keeping me busy. I am not seeing my wife overly at the moment
"The final 10 names are invariably what selection is about," he said. "We've got to make sure we get the chemistry just right."
This Saturday's EDF Energy Cup semi-finals, featuring Gloucester against Ospreys and Cardiff Blues against Northampton, offers an opportunity for McGeechan to guage the form of plenty of candidates.
The Heineken Cup quarter-finals in a fortnight, with the two Welsh regions the Ospreys and Blues, English sides Leicester and Bath, plus Irish provinces Munster and Leinster, also provide a stage to impress.
McGeechan has stressed that only players who are fit and in form will be included in the party that leaves for South Africa on 24 May.
That may mitigate against the late inclusion of Jonny Wilkinson, whose comeback for Newcastle after six months out with a knee injury has been delayed by at least another week.
The England fly-half, a Lion in 2001 and 2005, has only three Falcons matches left in which he could participate before McGeechan names the squad.
"We need to leave for South Africa with 35 players fit and ready to play," McGeechan told the Daily Telegraph. "If someone selected then picks up a four-week injury just before we depart, they'll have to go on standby."
Another player currently sidelined, Wasps wing Paul Sackey, has not given up hope of making the squad despite losing his place in the England side.
Sackey has resumed running after a leg injury sustained against Ireland during the Six Nations, and hopes to return in Wasps' Premiership game against Wilkinson's Newcastle a week on Sunday.
"I still think I can play my way back into the Lions squad," he said. "If I can get fit and start playing well again then there is a chance of getting in on the back of my form throughout the year."
The Newcastle game will be the third for Wasps in the space of eight days starting at Saracens on Sunday, meaning McGeechan has his hands full juggling the demands of his club role with Lions duties.
"It is keeping me busy," he told BBC London. "Put it this way, I am not seeing my wife overly at the moment.
"I have been managing a couple of days a week at the club, but other days I have been travelling around on Lions business.
"A lot of things are in place but obviously selection is the key thing now."