The Giants said Tuesday that family friends informed them of his departure.
He told the newspaper his father was taken to a Las Vegas hospital with chest pains and died while being treated Monday.
Jim Fassel, the 1997 NFL Coach of the Year, guided the Giants from 1997 to 2003, submitting a 58-53-1 record. He was 2-3 at the postseason, including a 34-7 loss to the Baltimore Ravens in the Super Bowl in February 2001.
Fassel's 58 successes put him behind Steve Owen (153), Tom Coughlin (102) and Bill Parcells (77) among Giants coaches.
Fassel coached several outstanding players for the Giants, including Hall of Famer Michael Strahan. Strahan, now a co-host of"Good Morning America" and a tv character, called Fassel a significant part of the life.
"Just a fantastic man, fantastic coach, and he'll be missed," stated the former defensive end, who sent condolences to the Fassel family during Tuesday's GMA broadcast.
"I liked enjoyed every second with him as my mentor and following my livelihood when we continue to remain in touch and speak," Strahan said.
Former Giants running back Tiki Barber was one of those to pay tribute to Fassel on Twitter, writing,"He challenged me to excel in the small things, then allowed me run with the big ones."
Present Giants trainer Joe Judge talked of Fassel's ties to the group during minicamp Tuesday.
"That's something which makes you sort of sit back and reflect. It brings up a great deal of great coaches that have been through here," Judge said. "Look, it's definitely an honor to be in precisely the same position as all of these coaches."
Fassel was born in Anaheim, California, on Aug. 31, 1949. He played quarterback at Fullerton College, USC and Long Beach State. Back in 1972, he had been drafted in the seventh round by the Chicago Bears. He played in the NFL and World Football League.
Fassel was considered an offensive expert and worked for the Giants as offensive coordinator in 1991 and'92. He was the coordinator using the Denver Broncos, Oakland Raiders and Arizona Cardinals before returning to New York as head coach after Dan Reeves was fired.
He turned things around, posting a 10-5-1 mark and leading New York to the NFC East title, its first since winning the Super Bowl under Parcells in February 1991.
The Giants missed the playoffs the next two seasons. They seemed headed into the postseason in 2000 after launching with a 7-2 record, but consecutives declines to St. Louis and Detroit in November had lots of thinking the team was going to fold.
Fassel had other ideas. On Nov. 22, four days prior to a game with Arizona, the trainer put his reputation at stake, telling the media to target him.
"I will take full responsibility. I am increasing the stakes at this time," he explained. "This is a poker game, I am shoving my chips into the center of the table, I am increasing the ante. Anybody wants out, get out. This group is going to the playoffs. OK. This team will the playoffs."
The Giants defeated Arizona 31-7 and finished the regular season on a five-game winning steak that gave them the NFC East title with a 12-4 record. Playoff wins over Philadelphia and Minnesota followed before the Ravens crushed them at the Super Bowl.
New York missed the playoffs in 2001 and left it as a wild card in 2002, but Fassel dropped the group in 2003 and declared two games before the end of the year he would not be returning.
"On behalf of the Mara and Tisch families and our whole organization, I want to convey our condolences to the Fassel household and Jim's buddies. We were saddened to hear of Jim's passing. Jim was a good man and his record because our coach speaks for itself," Giants co-owner John Mara said in a statement. "Jim distinguished himself by the way he managed our staff and devoted his efforts to the fire fighters and other households following the tragedy of 9-11. The players admired Jim and enjoyed playing for him and his coaching staff. And we appreciated his seven decades of leading our team"
Coughlin was hired and led them to Super Bowls after the 2007 and 2011 seasons.
Fassel played college soccer before a short career in the NFL and Canadian football. He was also part of the coaching staffs at Denver, Oakland, Arizona and Baltimore, in Addition to head coach at the University of Utah. He never served as a head coach in the NFL again, but was the head guy for the United Football League's Las Vegas Locomotives.
Fassel combined Westwood One radio as a color commentator for its Sunday NFL games in 2007. He stayed with the community for two seasons, calling Sunday afternoon games with Harry Kalas and"Sunday Night Football" with Dave Sims. Fassel was also a part of Westwood One's playoff coverage those two decades, calling various games, and functioned the 2007 and 2008 NFC Championship Games.
John Fassel won't be in the Cowboys' minicamp this week after his dad's death. Fassel's assistant, Matt Daniels will conduct the special teams' portions of practice.
"John's as large of a family person as we've got here and our heart goes out to him and his family right now," Cowboys coach Mike McCarthy said. "John's love for his loved ones and especially his dad, Jim, he's shared several stories just in our brief time together."