Vermeil, who guided the Eagles to their first Super Bowl appearance after the 1980 season, said that he watched almost every game this season. He thinks Kelly has only scraped the surface.
"I like Chip's leadership style," Vermeil said. "He doesn't take himself too serious. He knows he's smart. He knows he can coach. He has confidence. He isn't negatively influenced by things done in the NFL by other people.
"He goes and does it the way he thinks it ought to be done, and it's a little different. It takes courage to do that. I didn't have that courage initially. I was a little intimidated by how they did things in the NFL. And I respect him for that."
After a burnout with the Eagles and a 15-year hiatus from coaching, Vermeil returned to the NFL in 1997 as head coach of the St. Louis Rams. Two losing seasons followed, but Vermeil found a quarterback in Kurt Warner, and the Rams, with one of the most potent offenses in NFL history, won the Super Bowl in 1999.
Vermeil said that he thinks the Eagles could reach the Super Bowl next season with Nick Foles at quarterback.
"But you need more than just Nick Foles," Vermeil said. "You need more than just one quarterback. But it sure makes a difference if you have a good one. And I think he might be that guy."
The Eagles lost one from their family on Tuesday when former team president Harry Gamble died at the age of 83. It was Vermeil who first gave Gamble a job in 1981 as a volunteer assistant after Gamble was fired as Penn's head football coach.
"He had a salary coming, so he called and asked if he could come over and help, so I brought him over and let him help, and eventually he went on salary and eventually he became GM," Vermeil said.
Gamble was promoted to director of football operations in 1984 - two years after Vermeil stepped down as coach. But they remained friends, even if they had drifted apart in later years.
"Just a nice man with good leadership qualities and great integrity," Vermeil said. "He [had] been fighting illness for a while. I appreciate having had the opportunity to get to know him."