A clause in the 23-year-old's loan terms would allow him to return to Anfield in January, with the Reds short on forward options following Fabio Borini's foot fracture
Fabio Borini is set to be out for around three months following an operation on a fractured bone in his foot, meaning that Luis Suarez is the only senior frontman on the Reds' books.
But the Northern Irishman insists that he has not given thought to bringing Carroll back, despite Hammers co-owner David Gold admitting on Thursday that the 23-year-old could be recalled in January.
"It isn't something I have considered, to be honest," Rodgers told reporters.
|15/2||Liverpool are 15/2 with PaddyPower to score no goals against Reading
"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."The Reds boss went on to underline the importance of keeping Suarez fresh, despite the Uruguayan forward's desire to play every game.
He explained: "I've rested him a couple of times knowing the squad we have and the games we have, looking to prioritise, but, like most footballers, he wants to play every minute of every game.
"It is something I need to assess. The most important thing is winning games - that is what we need to do and in order to do that as often as we can I need the best players on the field.
"Luis will absolutely love playing three times a week but I need to try to nurture him because there are still many games to play between now and January.
"And even in January if we bring someone in it may not be January 1, so that is something which, over time, I need to assess and we'll look to manage the squad."The former Swansea City boss also refused to criticise his superiors over the failure to land striker Clint Dempsey in the summer transfer window, before expressing excitement over the young attacking options at his disposal.
|"Luis will love playing three times a week but I need to nurture him because there are many games to play between now and January"
- Brendan Rodgers on Luis Suarez
"The reality is it has happened so we have to deal with it. I'm not going to cry over it," Rodgers continued. "It leaves us a bit short, there's no getting away from that, but it's what we've got so we'll just crack on.
"If anything else happens it will provide an opportunity for another player. We have other players that we may be able to have some flexibility within the team," he said.
"It is great for me to see the young players: Adam Morgan scored a couple of excellent goals for the reserves and Samed Yesil is a goalscorer. It is just a case of weighing up whether they come in or not.
"Not every young player can play: this is an unforgiving league and my job is to nurture the talent and not destroy it."