Centre has been an ongoing problem position for England ever since World Cup-winner Greenwood retired five years ago and Saturday's 19-9 defeat against Wales suggests manager Martin Johnson is still no closer to finding the solution.
Greenwood has questioned the balance of England's midfield and feels they could pay the price in New Zealand if the likes of captain Mike Tindall, Shontayne Hape and new cap Manu Tuilagi all play together.
"I don't think you can carry three big lumps," said the 38-year-old, speaking at Twickenham to promote the second Help for Heroes benefit match, which this year will pit the Northern Hemisphere against the Southern Hemisphere.
"The balance isn't quite right.
"However, we're not on Mars here. We're round the corner from nailing it."
Fellow World Cup winner Michael Lynagh, who helped Australia to victory in 1991, agreed the balance of England's midfield was wrong and called for one of Jonny Wilkinson and Toby Flood to play there.
"I quite like the idea of Flood and Wilkinson playing together," he said.
"Take your pick, 10 or 12.
"They both know each other very well, they've got great passing games. They both kick well."
Lynagh acknowledged it was a bit late in the day for such a radical rethink, but added: "It's a bit late in the day to be throwing in Tuilagi."
Greenwood declared himself "very, very bullish" about England's World Cup hopes, despite accusing them of bottling it like USPGA runner-up Jason Dufner in Saturday's warm-up defeat.
Greenwood, who watched England blow chance after chance to kill off their opponents at the Millennium Stadium, also tuned in for the last golf major of the year on Sunday to see Dufner throw away what appeared certain victory in the final few holes.
It was very much a case of deja vu for former Harlequins star Greenwood, who insisted England deserved to have their wastefulness punished by Wales.
"Being a humble Englishman leaving Cardiff on Saturday night, they thoroughly deserved their victory," he said.
"For England, I don't think it's a case of throwing the baby out yet with the bathwater.
"They showed some tremendously powerful passages of play, some tremendous opportunities manufactured.
"But as Jason Dufner found out in the USPGA last night, you can drive for show but it's all about putting when it comes down to the big events, and rugby's the same.
"You can get yourself in the right position, you can find yourself with all the territory in the world, but if you can't get across the blooming white line then life becomes very difficult.
"So there are some questions that Martin Johnson still has to resolve.
"But not being one-eyed, not wearing rose-tinted spectacles, I still, still believe that this is a very, very good England side, a very powerful England side.
"And when they get the confidence to play with ball in hand 20, 25 yards out, I feel as though they are going to score.
"I think they will suddenly turn themselves into a side that no-one, absolutely no-one - not even New Zealand - will be comfortable about playing in a knockout stage.
"I'm very, very bullish."
Greenwood predicted a "big reaction" to Saturday's defeat when England play their final warm-up game in Ireland.
However, they have not won in Dublin since 2003's Grand Slam decider and were easily beaten trying to complete a clean sweep in March's final RBS 6 Nations match.
Defeat there a week on Saturday would therefore be their third in four matches, arguably undoing all the good work of the past 12 months.
However, England went into the last World Cup in much worse shape and still managed to battle their way to the final.
That was pointed out today by Jason Leonard, the world's most capped forward and Greenwood's team-mate in England's triumphant 2003 side.
Leonard is hoping to convince some of the stars of the tournament to take part in the upcoming 'Heroes Rugby Challenge' at Twickenham on December 3.
The fixture, which was announced on Monday, follows the success of the same event three years ago, where 52,000 spectators helped raise £1.46million for Help for Heroes.
This year's match will see a Northern Hemisphere XV tackle a Southern Hemisphere XV, with each team containing professionals and ex-professionals as well as rugby-playing members of the armed forces.
Gilbert has released a new line of rugby cleats. The Gilbert Virtuo 8S is part of the exciting new product. Check it out.
The Barbarians are one of the top invitational rugby sides with a long history and classic rugby jersey.
The Nike Tiempo is a solid rugby cleat and one of few styles still made from full-grain natural leather.
The Lions get ready for their matches with this green training jersey. It's what the players wear. Get in the Gear!
A cool looking all black rugby cleat with the high performance adidas is known for. Get in the Gear!
Wear the crest of the British and Irish Lions on your t-shirt. A great look for the summer.
The Lions are ready to get their Australia tour underway. They arrive in Perth on Monday.
The New Zealand All Blacks training jersey for 2013/14. Get in the Gear!
The USA Rugby Pro Alternate rugby jersey is perfect for any fan of the Eagles. Get yours to wear during the summer Test matches.
The NEW All Blacks 2013/14 jersey has arrived at World Rugby Shop. Dare to wear the colors of the All Blacks.