Son suffered the injury during Spurs' 2-1 win at Marseille in midweek, for which he had surgery on Friday.
Conte ahead of the weekend said there was "no decision" made on Son's availability for the World Cup but, on Sunday, appeared more upbeat on the forward’s chances.
The World Cup starts two weeks today but South Korea's first game is four days later, giving Son more time to prove his fitness.
Conte told reporters: "With Sonny, I sent him a message after the surgery.
"Sonny was really, really disappointed with this situation but I hope for him to recover very well and to play in the World Cup because I was a player and I know the importance of the World Cup.
"I'm confident that he can come back quickly and play in the World Cup. He's not in hospital now he's home."
Spurs host Leeds next week before the six-week World Cup hiatus, before traveling to Brentford on Boxing Day in a game Son would hope to be fit for.