The Colombia midfielder has been strongly linked with a move to Chelsea in recent weeks following some impressive performances for the Milan giants this season.
Ausilio revealed the Premier League club have contacted Inter to express their interest in Guarin, but stressed they they are not planning to offload the 27-year-old.
"Guarin is an Inter player and we are happy to keep him," he is quoted as saying by the Daily Express. "Denying the contacts with Chelsea would be denying the evidence. It is a source of pride to talk with them about one of our players, but everything stopped there.
"We are happy Guarin could stay with us for a long time. We don't have the intention to sell him. He's an important player."
Guarin stated last month that Chelsea boss Jose Mourinho had been in touch with his agent, but the Porto man stressed that he is not looking to engineer a move away from the San Siro.
He said at the time: "I haven't spoken to Mourinho. My agent has done that.
"I hope that Inter are thinking about how much I really want to stay here.
"There is something going on, I can definitely not deny that.
"But now I focus only on Inter and to do well here, we'll see in the future."
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