The thinking is that the biggest free-agent priority is positioning themselves financially for four promising defenders whose contracts expire after the 2016 season: linebackers Jamie Collins and Dont'a Hightower, defensive end Chandler Jones and cornerback Malcolm Butler. So if the Patriots break the bank in free agency, it would be a surprise if it's for anyone outside that group.
Thus, whatever moves the team makes outside that group will likely be in the mid- to low-level to address a need, and here are a few lesser-discussed players from other clubs who might fit the bill:
TE Dwayne Allen -- The 6-foot-3, 265-pound former Colt is a combination player who has made plays in the passing game and also as a blocker. He had a career-high 45 receptions as a rookie in 2012, but wasn't as involved as a pass-catcher in 2015. Bill Belichick has spoken highly of him in the past.
DT Corbin Bryant -- A restricted free agent in Buffalo, the 6-foot-4, 300-pound Bryant has played in every game but one over the last three seasons, starting 10 in 2015. If he's tendered at a low level by the Bills, who are tight to the cap, he'd essentially be an unrestricted free agent because he entered the NFL as an undrafted player (the Bills would have a chance to match any offer, but could struggle to do so based on their cap situation).
WR Chris Hogan -- Scheduled for restricted free agency in Buffalo after totaling 77 catches in the last two seasons, the 6-foot-1, 220-pound Hogan is a physical target and solid route-runner who has had past success against New England (e.g. 6 catches for 95 yards on Nov. 23 in 2015 game). If he isn't tendered an offer by the cap-strapped Bills, he'd become an unrestricted free agent. Like Bryant, he entered the NFL as an undrafted player.
DT Steve McLendon -- The 6-foot-3, 310-pound McClendon, out of Troy, has been with the Steelers since 2010. He's started 30 games over the last three seasons. For a Patriots defense that plays multiple fronts, McClendon -- a nose tackle in Pittsburgh's 3-4 scheme -- could add another strong piece in the middle.
WR Rod Streater -- The five-year veteran had 60 catches for 888 yards and four touchdowns in 2013 for the Raiders, but has fallen off the radar since -- first because of injury in 2014 and then as a result of a scheme/coaching change and stacked depth chart that remained healthy in 2015. He's the type of undervalued asset on the market that could be appealing to the Patriots at a position of need.