According to ESPN's Josina Anderson, the Patriots "aren't rushing into anything" in the hunt to find a successor to the 42-year-old.
The search could begin internally with Jarrett Stidham and Cody Kessler, who are the two quarterbacks currently under contract with the team.
Stidham was a fourth-round pick in 2019, and based off his age and spot on the depth chart, he could be viewed as the in-house replacement.
The expectations have to be tempered for whoever starts the 2020 campaign for the Patriots, but they might be even lower if they are led by a second-year signal-caller with minimal in-game experience.
Head coach Bill Belichick and his staff could also go out on the quarterback market to bring in a veteran to either start right away or challenge Stidham for the starting role.
Andy Dalton could be a trade target, as it appears likely he will be replaced by presumptive No. 1 overall pick Joe Burrow.
The 32-year-old has thrown for 3,000 yards in eight of his nine NFL seasons, including 2019 despite his changing role, and he has recorded over 20 touchdown passes in six of those campaigns.
Dalton is scheduled to make $17.5 million in 2020. The decision to acquire him could come down to how much the Patriots want to pay a veteran quarterback, if that is their strategy.
With Tampa Bay set to announce Brady as its quarterback, the Patriots could dip into the free-agent market to acquire Jameis Winston, but he would also come at a significant price.
The 26-year-old made $20,922,000 in 2019, which was the final year of his deal with the Buccaneers.
Just like Dalton, Winston could come at a significant price that the Patriots may not be willing to spend on a quarterback.
The other possible solution is using a draft pick on a signal-caller to compete with Stidham. New England owns the No. 23 overall pick in the 2020 NFL draft and would have to trade up to select one of the top quarterbacks in the draft class.
Burrow, Tua Tagovailoa, Justin Herbert and Jordan Love are all projected to land in the top 13 in the latest mock draft from Bleacher Report's Matt Miller.
Jalen Hurts, Jake Fromm and Jacob Eason are the next three players on Miller's positional rankings.
The Patriots also have to worry about who will be protecting their future quarterbacks.
According to The MMQB's Albert Breer, the Patriots "have discussed a long-term deal" with Joe Thuney, who received the franchise tag Monday.
The 27-year-old is scheduled to make $14,781,000 in 2020 under the franchise tag, and an extended deal would not come cheap for the Patriots.
While a long-term decision has not been made yet, tagging Thuney was one of the decisions that put salary-cap constraints on future moves.
As WEEI's Ryan Hannable noted, the Patriots have less than $10 million in cap space, which could be a major factor in their decision-making on a replacement for Brady.
Follow Joe on Twitter, @JTansey90.
Statistics obtained from Pro Football Reference.
Contract information obtained from Spotrac.