Romero suffered a hamstring injury while on international duty with Argentina last month and has missed Spurs’ last two games.
The 23-year-old, named Italian Serie A’s best defender last season, joined Spurs from Atalanta this summer and has made 13 appearances across all competitions.
"The news is not positive. Not good," Conte said at a news conference previewing Tottenham's home Premier League clash with Brentford on Thursday.
"The injury is serious. I think it'll take time to see him again. Surely next year. We need to check his injury week by week but the injury is serious.
"Now he's trying to recover but he needs a long time to recover. It's a pity because you know he's an important player for us. The injury is very serious."
Pressed on when exactly he expects to see Romero back in action, Conte replied: "Next year. Next year. January, February, I don't know. But for sure in 2021 he has finished.
"We have to wait and see his recovery but the injury is serious."
Tottenham have won one and drawn one of Conte’s first two Premier League games in charge.
