With Brady entering the winter of his career, it wouldn't be surprising to see the Patriots sign a quarterback who they believe can be Brady's heir.
Cooks only lasted one season on the Patriots after he was traded from the Saints.
The Patriots might be in the market to draft another quarterback in the early rounds this year after trading Brady's former backup, Jimmy Garoppolo, to the San Francisco 49ers last season.
While New England doesn't pay strictly based on projected production, they like to ensure their veteran stars are not outpaid by out-of-house options, unless those newcomers slot clearly above the veterans in the pecking order.
The Rams will be without a first-round pick for the second consecutive year.
Cooks, a 24-year-old Stockton native, was drafted by New Orleans, then traded to New England in March 2017.
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While he wasn't a disappointment for the Patriots, the No. 23 pick in the 2018 NFL Draft is a high price tag for Cooks and New England can feel good about the return. Now in 2018, with Cooks due $8.5 million on the fifth-year option from his rookie deal, they now sit at 23 in the first round of 2018.
This gives the Patriots five picks in the first three rounds, with two firsts and two seconds.
National Football League draft intrigue: The first night of the draft will be even more interesting with the Patriots holding two first-round picks. Here are the latest details on the Cooks' trade and what the Patriots are getting in exchange.
Some think the Patriots could package those picks to move up in the draft and select one of the top quarterbacks as a future replacement for Tom Brady.
With Cooks gone, the Patriots have a hole at receiver. But moving on from Cooks certainly can't cause as much trouble with No. 12 as it would if they jettisoned, say, Rob Gronkowski or Julian Edelman. After Sammy Watkins received a huge deal from the Kansas City Chiefs, the Rams needed to find his replacement.