The Giants used the non-exclusive franchise tag on Pierre-Paul last month for a one-year contract worth $16,934,000.
The new deal for the star pass rusher reportedly will be worth around $17 million per year, with $54 million in guaranteed money.
The deal also will free up much-needed salary-cap space for the Giants, who were just $3,918,376 under the cap as of Friday morning, ESPN reported.
Pierre-Paul denied the reports of the deal, posting on Twitter: "What the heck is people talking about I ain't sign nothing. ... That's New York media for yah!! They always want the story first and they got it wrong."
The 28-year-old Pierre-Paul lost his right index finger and badly damaged the rest of his right hand in a Fourth of July fireworks accident in 2015. He was limited to eight games that season and finished with one sack and 26 tackles.
The 6-foot-5, 278-pound Pierre-Paul bounced back with a strong 2016 season, registering 7.0 sacks in his first 11 games before he was hurt against the Pittsburgh Steelers in Week 13. He underwent hernia surgery in early December and was lost for the rest of the season.
A first-round pick (No. 15 overall) out of South Florida in 2010, Pierre-Paul twice made the Pro Bowl and registered a career-high 16.5 sacks in 2011. He has 50 career sacks in 95 games.