The fly-half sustained the injury while taking a kick during England's 23-13 RBS 6 Nations victory over France.
Head Coach Stuart Lancaster has revealed Farrell is making good progress but he insists he will take no unnecessary risks for the Azzurri clash.
"We have to make sure that the injury has healed properly so that it doesn't break down again through kicking," said Lancaster.
"There's no such thing as breaking yourself in as a fly-half, you're either fit or not.
"We'll give him time, but equally there comes a point in a week when we run combinations [in training]."
Toby Flood is likely to pull on the number 10 jersey if Farrell does not recover in time.
"Toby Flood trained really well today and is a good player for us, so I'm not worried in that regard," added Lancaster.
The England head coach also admitted No.8 Ben Morgan will not recover from his ankle injury to face Italy on 10 March.
They face Wales in the final round on 16 March and will be hoping they will be playing for a first Grand Slam since 2003.
But forwards Alex Corbisiero, Tom Croft, Calum Clark, Tom Johnson and centre Jonathan Joseph will not be fit for either of last two Championship encounters.