Gloucester try machine Simpson-Daniel, a strong candidate to make England's starting XV, is battling with a rib injury, while Northampton star Thompson has an ankle problem. Both players missed Saturday's English Premiership action.
Woodward is already without fly-halves Jonny Wilkinson (shoulder) and Charlie Hodgson (knee), centres Mike Tindall (ankle) and Stuart Abbott (ankle), prop Julian White (knee) and flanker Lewis Moody (foot).
Bath's World Cup back Mike Catt, meanwhile, is effectively out of the England equation, having been sidelined since late November, but there is much better news for Woodward surrounding injury-hit scrum-half Matt Dawson.
Dawson, troubled by calf and shoulder injuries since the World Cup, played for Northampton on Saturday, emerging unscathed.
And Dawson could find himself alongside Saints half-back partner Paul Grayson when England run out at Rome's Stadio Flaminio.
England's great fly-half debate will soon be resolved, with 32-year-old Grayson favoured in many quarters to take over from World Cup hero Wilkinson, who has been ruled out of the entire RBS 6 Nations tournament.
Wasps No 10 Alex King, Bath prospect Olly Barkley and Gloucester's in-form Henry Paul also have strong claims, but Woodward seems set to opt for experience by going with Grayson.
"There has been a lot said about Jonny, me, Paul Grayson and Olly Barkley over the past week," said five times-capped King.
"But you cannot think about it until it is announced, because it is not in your control. All you can do is wait until things happen, but it's nice to be thought of at the moment."