And now approaching the end of May, it seems rather unlikely that the two sides do come to an agreement for a variety of reasons. However, there might still be a sliver of hope remaining.
The Athletic's Connor Hughes reported on Thursday that the Jets "haven't shut the door" on the possibility of adding Sherman.
Despite all signs points to Sherman eventually signing elsewhere, the Jets are still open to a deal if the veteran cornerback is willing to sign with the team.
The NY Jets remain interested in Richard Sherman — with a catch
While the Jets aren't opposed to the idea of adding Sherman, they're not exactly blowing up his phone either. Sherman has quietly fielded offers from a variety of teams this offseason, but he's biding his time and waiting for the right offer.
And although the Jets may be "in the mix" by definition, it's unlikely that the "right offer" comes from them.
As Hughes points out, Sherman is looking to sign with a contender for another chance at his second Super Bowl ring. The Jets are in the midst of a rebuilt and, while improved, likely won't be competing for a Super Bowl in 2021.
The Jets would have to make up for it by spending a little extra to sign Sherman, something that has never been a Joe Douglas specialty.
Given their lack of eagerness to sign Sherman or any veteran cornerback, for that matter, it's hard to see them outbidding every other team.
That means that they'd have to rely on the Robert Saleh factor to get it done. Saleh and Sherman have plenty of history which each other and both have spoken very highly of one another in the past.
There's mutual respect between the two, but would it be enough to convince a 33-year-old Sherman to sign with a team that has an outside chance of even finishing above .500 in 2021?
That's for Sherman to decide. But at least on the surface, it would appear unlikely.
The Jets could certainly use a veteran cornerback addition with the likes of Bryce Hall, Blessuan Austin, and Michael Carter II currently penciled in as their starters.
That's two fifth-round picks and a sixth-round pick, none of which have established themselves as starting-caliber players at this point.
Hall has the most promise and could very well develop into a quality player, but counting on him as the No. 1 cornerback in 2021 is a recipe for disaster.
Despite this, the Jets seem content with the young group of cornerbacks they have now. They're hoping that their improved pass rush and defensive scheme will make up for their lack of experience in the secondary.
Only time will tell if it pays off.
A Richard Sherman signing isn't completely out of the picture, but don't hold your breath either.