He had felt tightness in his upper glute, and after some brief physio work, sat out the rest of the session.
Wood took no place in training on Wednesday, instead stood on the sideline with the staff watching on.
But it's understood his condition has improved considerably this morning, and he felt no pain today.
He will be listed to start, but still needs to come through the warm up at Aviva stadium.
The conditions will make it extra complicated; one hour before the 7:45pm (local time) kickoff, it was a chilly four degrees, and is expected to drop even lower as the night progresses.
That increases the risk of straining or tearing a muscle, and will be taken into account by the team's medical staff and the player.
But his presence, if he does start, will be a massive boost. Wood is the most irreplaceable player in the All Whites – even more so than Winston Reid – and his ability to lead the line will be invaluable.
He's also an aerial threat, one of the best in the sport and his strength in holding the ball up will help the All Whites retain possession, in a match where that will be difficult.
Wood is also a physical presence in a relatively small All Whites team and will also be crucial for defensive set pieces.
If he plays, it gives him a chance to add to his 24 goals (from 56 games), as he is just five away from Vaughan Coveny's record.
Despite most of the focus being on Ireland's do or die Euro 2020 qualifier with Denmark on Monday, a crowd of around 20,000 is expected for tonight's game in Dublin.