The 51-year-old Italian coach smashed the club’s leaders after taking his team to a Serie A position in 2019-20.
Conte said he had not gained popularity or coverage in a “difficult year.”
Later, rumours in Italy claimed that he had asked about the long history of Juventus coach Maurizio Sarri, something Conte strongly denied.
Italian journalist Fabrizio Romano confirmed Conte would hold showdown talks with club chiefs, with his future at the club on the line.
Romano tweeted: “[There will be] a phone call between Antonio Conte and Inter President Steven Zhang.
“No resolution has been taken on his long term as Inter technician.
“The club and Conte will have at the end of the Europa League if it’s time to split up or continue together.”
Meanwhile, Conte told the Italian publication Ansa that he would sue the repubblica newspaper for suggesting that he had spoken to Juventus about a return to Turin.
Conte said: “Seeing today’s repubblica article, I will obviously deny talking to Juventus players and coaches asking them if Sarri will be fired.
“I will sue the user who wrote the article and the newspaper editor.
“I did a three-year mission at Inter.
“As I’ve done in my life, I’m going to paint hard and give everything I have to make this task a winning task.”
After the Serie A season game, Conte signed up for Inter.
He said: “It’s been a difficult year on a non-public level, very complicated.
‘I don’t think the players have noticed that their paintings have been identified and I don’t think I’ve noticed my identified paintings.
“We’ve all won very little club coverage.
“We want to grow and in all areas, adding off the court, and a great club deserves a bigger shield to its players.
“We’ll talk about all this at the end of the season. I have to meet with the president (Steven Zhang) and he’s in China right now.”
Conte continued: “It was very, very intense this year, difficult, and the boys did well to isolate themselves and create unity in us, despite the difficulties.
“I don’t like other people getting on the train and I’ve noticed a lot of them with Inter this year.
“We had to put up with all the shit for months and they didn’t give us protection.
“My challenge is that I have a vision, I see the path we have to take and I know what we want to do.
“Possibly it would be a lightning rod the first year, but if you’re not informed and you’re still making the same mistakes, then it’s crazy.
“If you want to close the gap with Juventus, you have to be strong on the court but especially off the court.”
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