Captain Lawrence Dallaglio and Rome hat-trick hero Jason Robinson will both face fitness checks in the build-up to Edinburgh.
The world champions arrived back at their Surrey training base on Monday following a 50-9 defeat of RBS 6 Nations Championship opponents Italy.
Woodward was due to announce the team on Tuesday, but that has now been put back a day.
England's medical staff will assess Dallaglio, who has a swollen hand after he was the victim of a stray Italian boot.
Robinson, meanwhile, experienced a problem with the middle finger on his right hand and flanker Joe Worsley's hamstring also requires monitoring.
Dallaglio would appear to be the biggest worry but there are thought to be no immediate concerns about either Robinson or Worsley.
It would be in keeping with England's recent luck on the injury front if their preparations for Edinburgh were affected.
Woodward has already seen his RBS 6 Nations plans hit by the loss of fly-halves Jonny Wilkinson and Charlie Hodgson, while Lewis Moody, Mike Tindall, Stuart Abbott and Julian White are also currently sidelined.
If Dallaglio was ruled out after just one game in charge since he regained the captaincy, then Gloucester prop Phil Vickery and Saracens flanker Richard Hill would lead the contenders to replace him.