A loan for Carroll doesn't make much sense to me. Rodgers has said plenty of times that he loves working with players, and also that he needs time to teach them how to play the game his way. If he sees a future for Carroll on this team then I would think that he would much rather have him here under his own tutelage then off somewhere else for a year. Plus, there is plenty of playing time to be had since we hardly have any strikers at all right now even including Andy.
I think either this is a way for Rodgers to tell other teams that he is available for sale, or a way to light a fire under Carroll and make him fight for a place in the team. I think the latter is much more likely, and it appears to be working.
http://www.telegraph.co.uk/sport/foo...n-Rodgers.html
If he does loan him out then I think it is simply in hope of him having a good season elsewhere and driving his price up.
I have to say, I really like everything Rodgers has said and done so far. If you have some time to kill at work or something, this is a great interview where he outlines some of his plans.