Ding,ding,ding. We have a winner.
The Bills would be silly to offer Williams big $$, prior to tomorrow. They might find out later they were bidding against themselves and burned up some needed Cap space.
All the same, don't dismiss the notion that Williams does wish to test Free Agency and score the big signing bonus to go with a good contract. He's 33 and this is probably going to be his last good opportunity.
If say Chicago offers him a solid 4 year deal without some insane signing bonus, TD may say " That's not bad, I could match that " and he'll sign back with us.
Sometimes it's wise to not panic and let the Market play itself out.