I like Dempsey, but at 29 and looking for a big move it's not the type of player Lambert is looking at as he's said himself. Not worth the fee or the contract he would be after.
However, in terms of Carroll, reading Rodgers latest comments, he really doesn't like him does he?! A punt on Carroll on loan with a reasonable buy in clause could be worthwhile, although we all know Liverpool will want to recoup most of there money, and he wouldn't be worth that IMO.