According to Corriere della Sera, Conte received an anonymous threatening letter containing a bullet recently.
Meanwhile, the Serie A club said in a statement to Italian news agency Ansa that "the letter arrived at the club and not personally to the coach".
Here are further details.
Inter said Conte didn't go in person to file a complaint.
"In relation to the news, Inter Milan states that Antonio Conte did not personally receive any threatening letters and, consequently, he did not go in person to file a complaint," the club statement said.
"It was the club that received a letter and in this kind of situation, it contacted the competent authorities."
Meanwhile, Gazzetta Dello Sport reported that an investigation has now been launched and the Italian is receiving police surveillance outside his home and at Inter's training ground.
Police are said to be investigating the incident and will test the envelope for fingerprints.
This could help them in a bid to discover the identity of the person.
Reports state that a video surveillance is set to be analyzed in case of another delivery.
Also, extra surveillance cameras will be installed in and around Inter's base.
Many feel it could be some attention seeker and the threats won't be that serious, but both Conte and the club are said to have been warned to be vigilant.
Conte joined Inter in the summer of 2019 and has had an excellent start.
The club is second in Serie A and is just one point behind his former club Juventus at the top.
The 50-year-old led Juventus to three consecutive Serie A titles from 2012 to 2014.
He also spent two seasons at Chelsea.
He won the Premier League and the FA Cup.
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