Jones limped off after just 20 minutes of the 31-5 defeat in Ireland on February 26 and was thought to be a real selection doubt for the Italy game.
But the Wales camp are delighted with the Clermont Auvergne star's progress.
If Jones is not fit then Cardiff Blues number 10 Nicky Robinson and Gavin Henson are standing by as possible replacements.
Wales were less upbeat about wing Mark Jones, who came off with bruised ribs in the Scarlets' 27-26 victory over Bath in the weekend's Powergen Cup semi-final.
Jones is rated only 50-50 to be fit, but they do have Shane Williams to fall back on after he came through a Celtic League match for the Ospreys on Friday night after missing out against Ireland with a dead leg.
"Stephen is progressing well. We are optimistic about his prospects for the weekend," said Wales physio Mark Davies.
"He is not going to take part in team training today (Monday). He is continuing his rehab with a pool session, but he will take part in one of the team sessions tomorrow.
"And we will know with a lot more clarity then his prospects for the weekend.
"We knew it was going to be seven to 10 days from the point of injury and so it has proved."
But on Mark Jones, Davies said: "Mark Jones has bruised his ribs and they are particularly sore at the moment. And he won't take part in active training over the next couple of days.
"And it is fair to say there are doubts over his fitness for the weekend. He is probably rated 50-50 at the moment.
"Alix Popham came off on Saturday with a strain to his shoulder but that's only going to hamper him for a couple of days and won't be a problem for the weekend."
Meanwhile, Wales skipper Gareth Thomas, who has been ruled out for the rest of the season with a neck injury is targeting a return in the summer.
Thomas is keen to make Wales's summer tour to Argentina.
"If things go well, I would like to think that I might make it for the second half of the Wales tour to Argentina," said the Toulouse full-back.