"The lads have picked up some really good results home and away. We continued that against Lithuania and now we have a tough game coming up, but we are full of confidence."
If Hodgson brought Kane into the starting line-up, he would have to dispense with the 4-3-3 formation that worked so well against Lithuania, unless he started Wayne Rooney as one of the two wide-men alongside Kane.
He is more likely to switch to a 4-4-2 diamond, with Kane and Rooney up front as a strike partnership.
Hodgson was giving little away about team selection for Italy, but he accepts he will face increasing calls for Kane to start after his stunning debut.
"If I listened to clamour every time then a lot of players would be playing from the start in the next game," said Hodgson, who has also released Raheem Sterling, James Milner and Leighton Baines from his squad.
"People come and go but I think Harry is here to stay.
"It could well happen (that Kane starts). We won’t have Sterling and Welbeck so his chances increase all the time."
Hodgson was keen not to burden the youngster with even more pressure although he admits the forward’s debut could not have gone any better.
"The word fairytale comes to mind and it’s great when fairytales come true in this way," Hodgson added.
"I’m delighted for him, he’s had a good week in training and we’ve been quite excited to see him.
"But let’s keep things in perspective, for him it’s been a whirlwind romance for him in terms of playing top-class football and, if anything, I would like to try and relieve the pressure on him rather than heap pressure on him."
The 20 players left in the squad were given the rest of Saturday off after a morning warm-down session and team meeting.
They will train again on Sunday, when Ryan Bertrand will join in after being called up as back-up for Kieran Gibbs.
Seven of the 17 players left in the squad are yet to reach 10 caps, so Hodgson knows stretching England’s winning streak to eight matches will be difficult.
"It will be an enormous test for the ones we put in because some of them won’t have played in the national team for a long time and they are going to be playing against a top team, but we need a good squad going forward and we need competition for places," Hodgson said.