Bears DT Akiem Hicks is a guy I'm curious to see if he gets cut for cap space. Some articles on the upcoming decision they have:

I'd definitely be hopeful of NE making a run at him were he to be released. He spent a year here in 2015 and here's his reflection on that:

As I recall, BB actually liked him a lot and was willing to match what he got in CHI. Deciding factor for Hicks was that CHI was going to let him play a full snap count while BB said he wanted to stick with rotating DTs to keep them fresher. So Hicks wanted the extra playing time to grow as a player.

Hicks by all accounts was a strong leader in CHI. There's been lots of chatter on "the patriot way" and all that. I think bringing back a guy who has positive things to say about it and good individual leadership qualities would be a god culture get. Obviously he could go the ring chaser route so NE would have to pay up to make it worth his while.