Rodgers is left with only Luis Suarez upfront after forward Fabio Borini was ruled out for three months with a broken foot. Liverpool have been linked with several strikers across Europe but have to wait for nearly two months until the January transfer window re-opens.
But even though Rodgers has the option to recall Carroll, he has not considered it.
"It's not something I've considered, to be honest," Rodgers was quoted as saying in ESPN.
Rodgers loaned out Carroll to West Ham in August with Liverpool linked to Fulham's Clint Dempsey. But the deal collapsed while the American striker joined Tottenham Hotspur on Deadline day.
"Andy's a player who has gone out to get games, and that's what's happened. Obviously, we have people watching Andy when he plays, and report back on how he's doing. But at this minute, Fabio's situation has just come up, so we'll assess it from there."
Rodgers has tried and tested youngsters for the UEFA Europa League and Capital One Cup but has relied on Suarez for all the games in the Premier League. However, the Uruguayan is ready to play thrice in a week but Rodgers feels that's asking a lot from his lone striker.
"Luis playing three times a week, he will absolutely love that, but I need to try to nurture him, because there are still many games I need to play between now and January. And even if we bring people in then, that may not arrive on Jan 1," Rodgers said.
Youngsters Samed Yesil and Adam Morgan are other options Rodgers has but the Northern Irishman is wary of physical demands the league throws at them.
"It's been great for me to see the young players. Young Adam has scored a couple of goals recently in the reserves. He did very well and scored an excellent game away at Middlesbrough and one in the home game against Fulham.
And obviously young Samed Yesil is a goalscorer. But it's just a case of weighing up whether they can come in or not. I've been able to do that with a few of the other players. As you've seen, if I believe they have that talent and personality then I will put them in," the Liverpool boss said.