Appearing on "The Waddle & Silvy Show" on ESPN 1000 on Thursday, Walton was asked if he would trade Noah for Anthony.
"No, unquestionably no," he said. "Joakim Noah is a championship-level player. He's the type of player who you can build a long-term future around.
"Whatever Joakim Noah is going to be involved in the rest of his life, he's going to be a winner at that level. I'm looking for guys who like to sacrifice. I'm looking for guys who care more about their teammates than themselves. That was Michael Jordan, that was Phil Jackson, that was Scottie Pippen … that's where you have to go. Go with the guys who believe in the bigger picture, not just looking out for their own selfish interest."