The Italy defender is being linked with Barcelona this month.
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Ausilio said: "If anyone wants Bastoni, they should call us and not go around talking about it.
"There is no indication that he will leave this summer. We are very happy with Bastoni and we are confident that he will continue to perform at a high level with us next season."
It's been suggested Inter will seek €60-70m to sell Bastoni this summer, with the defender being heavily criticised in Italy for his dismissal in their World Cup playoff defeat in Bosnia.
Bastoni also upset many just weeks before then, when he celebrated a red card for Pierre Kalulu against Juventus.