However, Jets coach Herman Edwards wanted to interview a few different candidates, and while doing so, the Redskins, and their new coach Joe Gibbs moved quickly and inked Williams.
If Edwards is disappointed, he is hiding it well.
"Gregg was one of the guys, but he was just one of six guys," said Edwards. "There is the process you need to go through."
Another top candidate for the job is Tampa Bay Buccaneers defensive line coach Rod Marinelli, but the Jets have yet to receive permission from Buccaneers to talk to him.
"They need to hire a GM first," said Edwards.
But even after Tampa Bay hires a GM, the Jets will have stiff competition for Marinelli's services from St. Louis assistant Lovie Smith, who is expected to land one of the vacant NFL head coaching positions. Smith and Marinelli are very close, and there is a better chance Marinelli would join Smith than Edwards.
On Thursday, Edwards will interview Baltimore Ravens secondary coach Donnie Henderson for the defensive coordinator job.
"Donnie is very thorough," said Edwards. "He has been in a good defense. He's been in the league for quite a long time. I knew him as a college coach. He is a demanding guy that gets after people. He has done a good job in Baltimroe with the secondary."
Another potential candidate for the job is former Pittsburgh Steelers defensive coordinator Tim Lewis.
"He could be an interesting guy," said Edwards. "I know his agent pretty good because he's my agent too."
Former Giants assistants Johnny Lynn and Denny Marcin have already interviewed for the opening, but are more likely being considered for position coaching slots; Lynn for the secondary and Marcin, the defensive line.
Edwards would like to interview Philadelphia Eagles assistant Ron Rivera, and Tennessee Titan assistant Gunther Cunningham, but will have to wait until those teams are eliminated from the playoffs.
"There can't be a timetable because teams are playing, so what are you going to do," said Edwards. "As long as teams keep playing, you have to wait. Patience is part of the process, you just have to wait."