Wood (ankle) and Parling (knee) picked up injuries in European action for Northampton and Leicester at the weekend.
Backs Brad Barritt (knee), Kyle Eastmond (shoulder) and Owen Farrell (knee) are also being assessed while Northampton centre Luther Burrell suffered a concussion against Racing Metro and will undergo the graduated return to play protocol with a view to taking part in full training later this week.
"The players will be fully assessed once they get into camp this evening and it’s too early to give any definitive news on their status," England head coach Stuart Lancaster said in a statement on Monday.
"Tom's ankle and Owen’s knee has been scanned. Owen will see a specialist this evening and we will be able to provide an update on him and the other injured players tomorrow, along with any other potential additions to the squad."
England start their Six Nations campaign against Wales in Cardiff on Feb. 6.
Lancaster is already without number eight Ben Morgan and lock Joe Launchbury for the tournament while lock Courtney Lawes has been ruled out for the first few weeks while he recuperates from ankle surgery.
Centre Manu Tuilagi, battling a groin injury, is set to miss the games against Wales and Italy.
(Reporting by Justin Palmer; editing by Alan Baldwin)
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