Why are you so sure they NEED a buyer?
They draft Williams, who might be amazing, but needs a lot of work. They run with Fields at least to the trade deadline, when a contending team might have an injury. It's not like they signed a really good vet QB, not a Brady-Winston situation, by any means.
I wouldn't move Fields, who's relatively cheap, while I'm trying to prepare a rookie QB. If Fields keeps improving and goes out there next year and lights it up, Chicago will get a haul for him at the trade deadline. Of if not that, they'll get a 3rd round comp pick when he signs elsewhere the following year for a boatload of cash.
Why in the world would you off-load those possibilities for a worthless 6th rounder?