Currently, the Bengals have about $20.5 million in cap space remaining for 2015, according to Over The Cap. It will drop to roughly $15M after the cost for rookies, and various low-key re-signings and outside signings. Remember that only the top 51 salaries count against the cap in the offseason, so most of the players signed to be "camp bodies" will not count against the cap.
The Bengals currently have 64 players under contract, i.e. already 51 salaries counting toward the cap. Plus, each of the upcoming new salaries that break into the top-51 (such as each of the future rookie salaries) will cause an old salary to fall out of the top-51 and no longer count toward the cap. So this saves the Bengals a bit in each case. Overall, it's clear that the rookies and low-key signings will not have much effect on the cap.
Of the roughly $15M left, a small fraction serves as an injury fund, used to sign players mid-season (e.g. Greg Little last year). In 2014, they spent between $2-3M in total for this. Let's assume it will remain about the same. What's left is an estimated $12M or more to use toward extensions in 2015 and to roll over to 2016.
According to Over The Cap, the rough estimated salary cap is $150M in 2016. The Bengals currently have about $80M tied up in 2016, meaning $70M in cap space. However, based on trends of the past few years, the actual salary cap is most likely going to be above Over The Cap's estimation, closer to $155M. Excluding any roll-over, the base cap space for 2016 is projected to be about $75M.
Based on my personal estimations, and discussing them with several intelligent Cincy Jungle posters, here are projected long-term re-signings and extensions for mildly important players that the team will explore the possibility of keeping. NOT that the Bengals will keep all of them, these are simply each of their estimated costs.
A.J. Green: $13M/year, or the projected $13M franchise tag
Kevin Zeitler: $7M/year, whether by long-term deal or fifth-year option
Andrew Whitworth: $8M/year on a shorter-term deal
Andre Smith: $7M/year
George Iloka: $6M/year
Dre Kirkpatrick: $7M/year (unlikely that his fifth-year option will be used)
Reggie Nelson: $4M/year on a shorter-term deal
Adam Jones: $2M/year on a shorter-term deal
Marvin Jones: $7M/year
Mohamed Sanu: $5M/year
Emmanuel Lamur: $3M/year
Vincent Rey: $2M/year
Brandon Thompson: $2M/year
Less important unrestricted FA in 2016 include: Leon Hall, Wallace Gilberry, Jayson DiManche, Chris Carter, Nico Johnson, Eric Winston, T.J. Johnson, Shiloh Keo, Chris Lewis-Harris, and Kevin Brock. The Bengals will not look to re-sign most of them, though they might re-sign a few.
The numbers for the 13 listed players above add up to about $73M. So assuming the projections are close to correct, the Bengals will be able to re-sign most of them. And they could re-sign all 13 if they truly wanted to. Not all 13 will be kept, and a few should be let go anyway, but this just demonstrates how much cap space the team has.
The Bengals have $20.44M tied up for 2015 in Rey Maualuga ($7.137M), Domata Peko ($3.7M), and Leon Hall ($9.6M). Unfortunately, Maualuga is one of the worst LB in missed tackle % and surrendered reception %, and Peko and Hall are shadows of their former good selves. It would've been ideal to use that money on extensions early on, and reasonably-priced quality free agents, and then pocket the rest for the future. Fortunately, in spite of this financial black hole, they still have enough cap space.
And that doesn't mean those three players are entirely safe in the near future. If the Bengals cut Hall and Peko later this offseason to get more cap space for extensions, they will save $11.5M ($9.6M for Hall plus $3.7M for Peko, minus $1.8M dead money for Hall). Cutting Maualuga next offseason saves $4.1M. And it's possible that Andy Dalton gets cut next offseason if the team wants to draft a new QB in 2016, initially saving $5.9M ($13.1M minus $7.2M dead money), and an additional $60M in the long run. If they want to, the Bengals can easily create over $20M additional cap space for the 2015 and 2016 offseasons from just a few contracts.
Overall, the Bengals have plenty of cap space both now and down the road, and can clear up even more if they want to. So for this offseason and next, they'll be able to keep everyone who they believe is worth keeping.