Icardi's deal runs through to the end of the 2020-21 season but the striker's agent and wife Wanda Nara claims two major clubs have expressed an interest in signing the 25-year-old.
Spanish and European champions Madrid are believed to be one of the side's eyeing the Argentina international, who has scored 18 goals in Serie A this season, while Manchester United were also linked with him this winter.
But Ausilio claims Inter have the resources to hold onto their top players, and that the club are in constant contact with Icardi over the prospects of keeping him at the club.
"We are in constant contact with Icardi's agent, aimed at the common goal of seeing if the future can be shared together and above all it'll be done in silence," he told Mediaset Premium.
"The more talk there is, the more decisions get bumped down the road.
"We want to engage in action, not words, and make sure everyone is in the right condition to give their best on the field.
"If you list all the players in the squad, you'll realise we are not that poor.
There are many big names here, including several watching from the bench, because this team was constructed with a certain logic to target a Champions League place."
Inter climbed up to third position ahead of Roma's showdown with AC Milan after recording just their second Serie A victory in 11 matches, but the next two weeks could be telling in their chase for a top-four finish.
The Nerazzurri face Milan on March 4 before facing league leaders Napoli the following week.