The 28-year-old was expected to be out of action for the rest of the campaign with a back injury but he has responded well to treatment and is already showing signs of making a speedy recovery.
Manager Claudio Ranieri said: "Veron has had the operation and we hope he will be back in the country this week.
"He is supposed to be out for three months but if everything goes positively well maybe we can cut that by one month"
Ranieri has also been boosted with the news that striker Hernan Crespo and midfielder Damien Duff should return later this week.