However, Ausilio would not confirm if a deal has already been reached with De Vrij and is currently focusing on the players already at the club.
"I cannot confirm anything," he said. "Inter's transfer window opens on May 20. First we will talk with our players and evaluate the players we have here."
One of those players is Mauro Icardi, with Ausilio reiterating that a deadline to agree a contract extension at San Siro has not been set.
Icardi has been consistently linked with European champions Real Madrid, but his agent and wife Wanda Nara spoke recently of her confidence in a new deal with Inter being signed.
There appears to be no rush from Inter's perspective, but Ausilio still shares Nara's optimism regarding the club captain.
"There's no deadline - everything with Mauro is so spontaneous that it could happen tomorrow the same way it could happen at the end of the season," Ausilio told Premium Sport. "It will be a very standard process.
"He might be getting a bigger [house]. He's happy here and his family have a good life in Milan. Inter have always shown him gratitude - it wouldn't be a surprise if we started discussing a renewal, it would already be the fourth time."
A late miss from Icardi meant Inter were held to a 0-0 draw by rivals AC Milan in the Derby della Madonnina on Wednesday.