The 30-year-old is coming off the back of his best season in personal terms, having scored seven times in 39 games as Torino finished 10th in Serie A and reached the quarter-finals of the Coppa Italia.
Leicester and Newcastle are looking to add to their squad in the close-season to improve on their own mid-table finishes in the Premire League and see De Silvestri - who can play as a full-back on either flank - as a good option.
“I had a great season at Torino and I am glad to see that people have noticed," he told Goal.
"I'm very happy at my club but it’s always a pleasure to know that there could be interest from the Premier League.”
Leicester have already begun shopping this summer, signing Ricardo Pereira from Porto last month.