Jonny Wilkinson has slipped down the pecking order thanks to his ongoing injury problems while Jason Robinson - his successor as England skipper - has struggled for form of late.
Munster second row Paul O'Connell was touted as an alternative but he has only captained Ireland on two occasions and although a good bet to make the Test line-up, he is not guaranteed a place.
Of the other Six Nations captains, Scotland's Gordon Bulloch may not even be second-choice hooker on tour while Wales skippers Gareth Thomas and Michael Owen are injured and inexperienced respectively.
The indications are that the job is O'Driscoll's - an appointment which would get the full backing of former Lions Test hooker Wood.
"Brian has toured before, he has guaranteed a slot and he has played really well in the Six Nations," said Wood, who was replaced by O'Driscoll as permanent Ireland captain when he retired after the 2003 World Cup.
"He's comfortable being an international captain and he has
the respect of all the players.
"Sounds like a captain to me really. If you are taking somebody else you are taking an element of risk that maybe needn't be there."