The tag deadline is 4 p.m. ET on Tuesday.
Both parties wanted to get something done, and the franchise tag could still act as a placeholder. Williams, 26, played on the franchise tag last season at $16.126 million. A second tag comes at the cost of 120% of last year's number, or $19.351 million.
Giants general manager Dave Gettleman was asked recently if the team could handle carrying Williams' nearly $20 million hit on the salary cap.
"It certainly makes it a little more difficult," Gettleman said. "But we'll operate and we'll manage."
It's still very unlikely the Giants go in this direction. They would need to make several major moves to be able to withstand that type of direct cap hit. Their intention is to sign Williams to a long-term deal, a source told ESPN.
Williams had a career-best 2020 season in which he finished with 11.5 sacks and 30 quarterbacks hits, good for third in the NFL. His 41 quarterback pressures were seventh among interior defensive linemen, according to NFL Next Gen Stats.
Williams was their best pass-rusher last season by a wide margin, producing more quarterback hits than the rest of the team's defensive linemen combined.
It was quite the turnaround for the former first-round pick of the New York Jets in his first full season with the Giants. He thrived under coach Joe Judge and in the defensive system of coordinator Patrick Graham.
Williams was credited with half a sack the previous season, which he split between the Giants and the Jets. It was the latest in an unspectacular first five years in the NFL after being the sixth overall selection out of USC in the 2015 NFL draft.
The Giants still traded a pair of midround draft picks for Williams midway through the 2019 season, just months before he was set to become a free agent. They placed the franchise tag on him last offseason.
Williams proved worth his 2020 salary -- and much more -- as one of the most productive defensive linemen in football. He produced the first double-digit sack season of his career, with his previous high being seven in 2016.
For his career, Williams has totaled 323 tackles and 29 sacks.
The sixth-year lineman has an unresolved grievance with the NFLPA, ESPN's Jeremy Fowler reported recently. It's a discrepancy over whether he should have been listed as a defensive end or tackle. If it's the former, his 2020 salary would have been $17.8 million. That would make his second tag subsequently worth $21.4 million.