Jared Allen should be the best option for the Bengals to go after with a little more aggression. He is almost 32 but has proven that he can still be a top tier talent. The only drawback is that he might be the best free agent of his position.
This means he might command more money than the Bengals are willing to pay. He would be well worth a 2 or 3 year deal, the problem may be what the cap hit may end up being. He is coming off of a 6 year/$72 million contract.
He would be brought in to start for the next few season. This means that they can focus on drafting positions that may be more immediate or even draft for depth. Jared Allen would be a welcome switch for the underperforming Michael Johnson. He has been able to not only stay healthy but works hard every play.