The Argentine international came off injured during the World Cup Qualifying draw with Brazil on Wednesday morning. The 23-year-old went to ground clutching the back of his leg and is a confirmed absentee for Sunday's game at Tottenham Hotspur Stadium.
"We've bad news about Cristian Romero about his injury," said Conte.
"I spoke to the doctors and now it's to wait 7-10 days for another scan to see how long it will take him to recover."
Romero is not Conte's only issue ahead of a meeting with Marcelo Bielsa's Whites.
Midfielder Oliver Skipp is suspended having picked up a fifth booking of the season against Everton and there are question marks over a couple of others.
"Giovani Lo Celso didn't come back perfectly physically and I don't know about him if he's available," said the Italian.
"Skippy was banned for one game but in the previous games we played with Skippy and Hojbjerg. I hope today to have Hojbjerg back with the team because he was away for the week, and then there is one between Winks and Tanguy [to play instead of Skipp]."
If Tanguy Ndombele gets the nod from Conte, he'll be expected to put in a huge shift for the team. The creative midfielder has recently come in for criticism from Spurs legend Glenn Hoddle for not understanding the game, despite having 'wonderful skills.'
"I have seen many managers struggle with his position," said Conte.
"He has the quality. He has to understand it is a team and he has to play into the team. It is important to do what the position asks you to do. We are working very hard. He has to work much more than the others. He has talent but he has to put it into the team for the team, not for the single player. Every single player has to know what he has to do. If every player just runs around the pitch, it will be a mess."