Turns out the quote wasn't hard to find. From 2017, as described by Urban Meyer after a coaching clinic where he and Belichick talked:
“I started asking him about it and he made this point to me and I shared it with our team. He said, ‘At this point in my career, I want to coach guys I like. I want to coach guys I want to be around and that’s it.’ He said, ‘I’m not going to coach anybody else.'”
And man, reading that gave me a sense of dread at the time. Kept drinking my coolaid but that quote always stayed with me, and not in a good way.