Cohen has already been ruled out of Northampton's Powergen Cup semi-final against London Irish on Sunday due to a thigh strain.
But Woodward has ruled out all but Jason Robinson and Trevor Woodman of those injured players from having a chance of making the Italy game.
"Of the injured players only Jason Robinson and Trevor Woodman may be available to play against Italy but this will depend on them continuing their rapid progress from injury," said Woodward.
Sale Sharks wing Robinson suffered a knee injury in last Saturday's win over Wales and Gloucester's Woodman is expected to make his comeback from three months out with a shoulder problem on the bench for the Powergen Cup semi-final with Leicester on Saturday.
England squad for training ahead of RBS 6 Nations Championship games against Italy on March 9.
Backs - J Lewsey (Wasps), D Luger (Harlequins), J Simpson-Daniel (Gloucester), J Noon (Newcastle), P Christophers (Bristol Shoguns), W Greenwood (Harlequins), M Tindall (Bath), O Smith (Leicester), C Hodgson (Sale Sharks), J Wilkinson (Newcastle, vice-capt), M Dawson (Northampton), K Bracken (Saracens).
Forwards: G Rowntree (Leicester), M Worsley (London Irish), R Morris (Northampton), S Thompson (Northampton), M Regan (Leeds), M Johnson (Leicester, capt), B Kay (Leicester), D Grewcock (Bath), S Shaw (Wasps), R Hill (Saracens), J Worsley (Wasps), A Sanderson (Sale Sharks), L Dallaglio (Wasps, vice-capt).
Players injured, but attending sessions: N Back (Leicester), I Balshaw (Bath), B Cohen (Northampton), D Flatman (Saracens), A Healey (Leicester), J Leonard (Harlequins), L Moody (Leicester), J Robinson (Sale Sharks), P Vickery (Gloucester), J White (Bristol Shoguns), T Woodman (Gloucester).