Head coach Bill Belichick has traditionally promoted from within in situations like these. If the Patriots stay in-house, the top candidates would be defensive line coach Pepper Johnson and linebackers coach Matt Patricia. Both have grown up in the Belichick system and bring strong qualifications to the job.
In terms of outside candidates, former Virginia coach Al Groh is one possibility to consider. Belichick talked this week about the value of having coaches who aren't afraid to challenge him, and Groh would qualify in that regard.
Pees coordinated the Patriots' defense the last four seasons. When he was promoted from linebackers coach to coordinator in 2006, players spoke about how they liked his veteran presence and communication skills.
Health might have been on his mind as he considered his future, as Pees had been hospitalized during the season finale after experiencing a shortness of breath. He checked out fine and returned home to New England the next day.
One aspect of this move to monitor will be if the Patriots consider alterations to Belichick's 3-4 scheme. However Belichick elects to fill the coordinator void -- either in-house or looking outside -- there is now an opening on the defensive staff and that could lead to some fresh ideas being considered.