The Ireland centre is aiming to become the first player to go on more than three Lions tours in the professional era.
And while Greenwood, who went on three tours of his own and was the last uncapped Lion, fears O'Driscoll will miss out on Test selection he is certain he will play a major role Down Under.
"Brian's probably just behind the blue ball in terms of selection for the opening Test team," said Greenwood.
"But if he manages his RaboDirect PRO12 season and goes well for Leinster he will have a chance.
"He missed virtually all of the season after getting injured at the World Cup. But he still does things that defy his age and against New Zealand he was magnificent in defence.
"Even if he doesn't get in the Test team there will be no one better to have in and around the camp than Brian O'Driscoll.
"He has such a strong affinity with the Lions. He scored that special try against Australia in 2001, 2005 was full off disappointment and then there was that huge hit on Danie Rossouw in the second Test against South Africa in 2009."
Only two players have achieved the feat in previous years - O'Driscoll's fellow Irishmen Willie John McBride and Mike Gibson.
McBride made five tours, between 1962 and 1974, playing in a staggering 68 matches in that time, while Gibson's record is equally impressive with his own quintet of trips and 66 matches.
Greenwood, who also replaced O'Driscoll just minutes into the infamous first Test against New Zealand in 2005, insists the Lions have a real chance of grabbing a first series victory since 1997.
And he reckons no one deserves to be part of that more than the Leinster, Ireland and Lions stalwart.
"Brian's had a fantastic career he's got everything in the locker but you really want a World Cup medal or a Lions series," added the England World Cup winner.
"The most realistic one for Brian now is the Lions and he deserves it. But Australia won't think that and they will want to send us packing"