According to BBC Sport, the England worldwide is facing a minimum of one month out with his latest injury, which will come as a big blow as Carroll was said to be keen to join the reigning Premier League champions.
The former Manchester City striker has impressed in Serie A with Roma this season, scoring nine times in the league so far, and that form has attracted interest from the Blues as Conte looks to bolster his attacking options in the January window.
The full-back has been linked with both Liverpool and Newcastle United, while Juventus are also keen, but it is Chelsea who are pushing to do a deal for the player. "This target is very prestigious for every team because this competition, the Champions League, is the biggest in the world for clubs".
"It is not right to talk about the characteristics of other players".
Additional reporting from Nizaar Kinsella, Goal's Chelsea correspondent.
His stats won't knock your socks off - he has only two goals in 12 appearances this season - but he's still got value. He's by no means a starting-caliber forward, and at the age of 29 is nearing the end of his prime years.
Conte was also questioned on whether Chelsea needed to bring in a tall striker to partner Morata up front.
With age comes experience, and Carroll has plenty of experience in the Premier League. "You are the first to know (the) news". They were out. But we must be ready, we must be ready to fight for a place in the top four.