Corriere dello Sport says Inter are interested in the Belgium international leading up to the winter market.
And Inter's pursuit has raised the possibility of a swap involving Cristian Chivu returning to his former club.
Ajax coach Frank de Boer revealed over the weekend: "Last summer we tried to get Chivu: he was the player who we chose to replace Vertonghen if he had left.
"Chivu in January? It will always depend on Vertonghen and Inter, who must decide to sell the Romanian. Chivu is an option of the highest level, a serious professional who has already played here and someone we have not forgotten."