The 23-year-old, who is currently on a season-long loan at West Ham United, is believed to have an agreement in his temporary deal which states that he can be recalled by the Reds in the winter window.
"[Bringing Carroll back] isn't something I have considered, to be honest," said Rodgers. "Andy has obviously gone out to get games. We have people watching when he plays and they report back on how he is doing. But with Fabio's injury just coming up we will assess it from there."
Meanwhile, the Reds are preparing to face Reading at Anfield this Saturday.