Not only is Portland asking for Joakim Noah, they're asking for Jimmy Butler, too. That trade heavily favors Portland and obviously Chicago is going to turn it down.
Aldridge is a great player and I think he's absolutely someone the C's should be looking at, but we simply don't have anyone to offer for Portland. They're looking to contend very soon, as demonstrated by their interest in Noah, and we simply don't have a Noah of our own to give back.