Of the teams on that list, only the Jets are seemingly without the cap space to make a serious push. Or are they? One way to afford this would be with a relatively modest signing bonus for an All Pro cornerback, say $15 million, and substantial guarantees in 2017 and 2018. So, for example, you might structure a five year contract for a $1 million 2016 base salary with a $15 million signing bonus, followed by four years in the mid teens. The 2017 season might be fully guaranteed, and the 2018 season mostly guaranteed, with 2019 and 2020 not guaranteed. Norman ends up with $16 million in cash compensation in 2016 and an average of something close to $16 million in annual compensation (a number he is rumored to be targeting), but the cap hit for 2016 would only be $4 million, a number the Jets could readily afford. Of course structuring it this way would result in two years (2017 and 2018) of crazy cap numbers in the high teens for Norman before the Jets could cut him without prohibitive dead money. Norman hits his numbers and gets lots of guaranteed money, the Jets get an All Pro cornerback at a bargain price in 2016 before overpaying in 2017 and 2018, but avoid a really long term commitment. It could work.
Of course, just because you CAN do something doesn't mean you SHOULD do it. This would be a difficult deal to swallow for the Jets. It would give the Jets by far the highest paid cornerback tandem in the NFL, not necessarily a good thing. It would also be giving at minimum a monster three year commitment to a cornerback who will turn 29 years old during the current NFL season, who fits best in a zone coverage scheme, which the Jets don't run, and who has really had only one good season in the NFL.
In the alternative the Jets might afford Norman by releasing Muhammad Wilkerson, which would enable them to structure the deal in a more front loaded fashion, with the ability to cut Norman without huge dead money possibly as early as 2018. In either case, however, the Jets would still be committing large amounts of guaranteed money and multiple years to an All Pro cornerback who unfortunately may not fit their scheme, may be a one year wonder, and may soon start to exhibit significant age related decline in his play.
On the whole I suspect not making a serious push for Norman is the better course of action. What about you? Would you make a serious push to bring Norman in? If so, would you backload the contract to get it done or let Mo go and lop off a year of the Jets' commitment to Norman? Or would you find a completely different way to afford Norman, like perhaps a highly incentive laden deal, and if so, do you think he would accept such a deal?