Rogers has voiced that he is open to Carroll, who arrived for a club record £35 million in 2011 but has struggled to find form or the back of the net, go out on loan.
“It’s something I would have to look at, I have to be honest,” the former Swansea manager said.
“Andy’s always going to be linked with clubs, whether he was here or not. He knows exactly where he stand, but I have had no inquiries about him.
“There are many things to going on loan. Is it going to be beneficial for the club?
“it gets them game experience and they come back a better player, a more confident one. Certainly more so than if they’ve been sitting on the bench for the majority of the season.”
Carroll scored just eight goals in 49 appearances for Liverpool, but has been rumoured to be n the line for a move to AC Milan, who he impressed with his performances for England during Euro 2012.