And given the way that negotiations reportedly went, it's starting to seem very unlikely that the two sides ever reach a long-term deal.
The Jets' reported offer to Maye made their intentions clear. They don't plan to pay him what he's looking for and what he likely will receive from another team.
It seems the two sides are preparing for an eventual split. Maybe not now. Maybe not in a few months. But it's hard to see Maye on the Jets' roster in 2022 unless one side budges.
That split could come via an eventual trade, a tag-and-trade, or simply by letting him walk in free agency. Either way, it feels inevitable.
That means the Jets could be looking for his replacement next offseason. And one potential avenue the team could explore is the 2022 NFL Draft.
If Maye departs, the only potential long-term piece the Jets have at the safety position is 2020 third-rounder Ashtyn Davis. The jury is still very much out on Davis and free-agent signing Lamarcus Joyner turns 31 in November.
The Jets need a replacement if Maye leaves. Here are four very early possibilities they could explore in next year's draft.