Isla spent the season on loan with Serie A rivals Juventus, helping them to the league title, but he is set to return to Udinese due to their co-ownership of the Chilean.
The 25-year-old only managed 16 appearances last season and Vagheggi says he is on the verge of a move to the San Siro.
"Isla to Inter is very probable. There are a few details to sort out first," he told TuttoMercatoWeb.
"There are a few details to sort out"