The Reds boss told ESPN that he will be speaking with the club's managing director Ian Ayre tomorrow to discuss the possibility of bringing in a new forward ahead of the transfer deadline.
"That was the understanding, that Andy would go and get some games," he said. "He obviously wasn't going to play regularly here but he'll go to West Ham and get some games.
"Hopefully that will enable us to complete our aims of bringing in a player tomorrow. I'll speak to our managing director Ian Ayre, who has done brilliant over the summer."
Rodgers went on to say that he hopes to bring in more than one player on Friday, but admitted that it may not be possible.
"We've got a number of targets but it's not always our choice," he added. "We certainly need help with one or two numbers, I hope we can do that tomorrow."
Carroll could make his West Ham debut during Saturday's home encounter against Fulham.