In New England's case there was some truth to them not seeing him as a great fit for Brady as he was not primarily a deep ball thrower (and hadn't been since Randy Moss was there). The main speculation here about Cooks was that Belichick wanted him when Garoppolo was the heir apparent. They also talked with Cooks' agent about an extension after 2017 but were
really far apart given New England does not spend big money on WRs, so they traded him for the Rams 1st rounder vs. seeing him walk after 2018 and netting a lower comp. pick.