The France goalkeeper is out of contract at the end of the season and the Spurs captain will be allowed to talk to foreign clubs about a free transfer from Saturday.
The 35-year-old arrived in north London from Lyon in August 2012 and Conte was confident he would stay with his squad.
“Hugo is a Tottenham player, he’s the captain,” he said. “For sure he will talk with the club to try to find a solution.
“I think Hugo wants to stay in his club, he loves the club, he stays well in Tottenham.”