According to ESPN's Field Yates, his sources have noted the following players as beginning camp on the Physically Unable to Perform list (PUP). This means they cannot practice, but will be able to use the team facilities. Players can be removed from the list at any time, but they cannot be added back.
CB Alfonzo Dennard
WRs Aaron Dobson and Jeremy Gallon
DT Tommy Kelly
ST Matthew Slater
That's the list. Dennard has missed plenty of time this off-season and has a history of injuries and is recovering from shoulder surgery. Dobson is still questionable with his foot recovery. Kelly is still working through his ACL recovery.
I'm assuming Gallon has a bad case of the Foxboro Flu, while I can't seem to find any reason why Slater has been missing time, although he was limited earlier in the off-season.
Best news? DT Vince Wilfork isn't on the list. Neither is TE Rob Gronkowski. Or LB Jerod Mayo. Or RT Sebastian Vollmer.
Note that the list isn't official and is just from the grapevine; but the fact that they're not immediately linked to the PUP list is a positive sign. This is your good news of the day.
The team has also announced the release of DT Seali'i Epenesa and the signing of DT Eathyn Manumaleuna. The 6'2, 300 lbs Manumaleuna is a four year starter from BYU, with experience at both NT and DE. He's 25 years old and took two years off in 2008-09 as a missionary; he also redshirted in 2012 due to a torn patella tendon. He's a camp body and is likely expected to fill the role of Tommy Kelly until the latter is ready to return.
Yates has also named DL Dominique Easley, RB Roy Finch, LB Deontae Skinner, and OT Chris Martin as players with the Non-Football Injury distinctino (NFI). This means that they were injured prior to their NFL career, which makes sense for Easley and Finch who were both coming off of college injuries, while Martin was picked up at the end of June after being waived by the Texans due to injury.
There's no real difference between PUP and NFI at this stage, especially with all rookies. Hopefully Easley can make it make to the field as soon as possible; it's likely he'll have to pass a physical once camp starts before he'll be cleared.