The Saracens prop had been expected to be called up to the side for the Twickenham clash on February 26 after missing the past two months with a knee injury.
It has been decided that Vunipola will instead continue to build up his fitness with his club side, and could play a part in Friday's Aviva Premiership match with Gloucester Rugby at the Kingsholm Stadium.
Jones intends to shake up his starting lineup for the visit of Italy in the third match of England's Six Nations title defence, as they look to make it 17 wins in succession.
England training squad:
Forwards: Jack Clifford, Dan Cole, Ellis Genge, Jamie George, Dylan Hartley, James Haskell, Paul Hill, Nathan Hughes, Maro Itoje, Joe Launchbury, Courtney Lawes, Joe Marler, Kyle Sinckler, Tom Wood
Backs: Mike Brown, Danny Care, Elliot Daly, Owen Farrell, George Ford, Jonathan Joseph, Jonny May, Jack Nowell, Ben Te'o, Anthony Watson, Ben Youngs