Sixteen days ago a writer at NFL.com released the team-by-team salary cap number, giving the Bengals a figure of $16,309,693. However since the Bengals have been largely inactive -- in every holy way imaginable -- that cap number hasn't shifted much. According to the team-by-team salary cap numbers released by Pro Football Talk, the Bengals have $16.30 million under the cap, fifth-most in the NFL as of this posting.
Aside from having a pool of money to sign players in response to injuries (which are bound to happen), as well as Brandon Thompson's contract (whenever that will be agreed on), the Bengals do not have any money scheduled that would dramatically affect the team's payroll and salary cap.
There is, however, reason to believe that contract extensions are on tap for players like Geno Atkins and Carlos Dunlap, who will be entering their final year under contract next season. Or much closer to guys like Rey Maualuga, Thomas Howard or Manny Lawson. Additionally the team will want to figure on more projected extensions on younger players that they'll need to keep if they want to promote sustained success. To keep those options open, the team probably doesn't want to smash the payroll too much before those deals are signed. But we're just conjecturing at this point.