Kelly met with the Eagles on Tuesday, and there was mutual interest after the interview, according to league sources. Kelly left the country after meeting with the Eagles and could not be reached for comment.
The Eagles and Kelly have agreed to revisit talks when he returns this weekend, according to league sources.
CBSSports.com reported Wednesday that the Chicago Bears also are interested in Kelly. But sources refuted that report to ESPNChicago.com.
Kelly coached the Fighting Irish to a 12-0 regular season and an appearance in the Discover BCS National Championship. Playing for its first national title since 1988, Notre Dame was routed by Alabama, 42-14, on Monday night.
Philadelphia has been seeking a replacement for longtime coach Andy Reid, who was fired one day after the Eagles completed a disappointing 4-12 season.
Kelly denied having any interest in an NFL coaching job this past Saturday, claiming that leaving Notre Dame "is not an option. I don't even think about it."
Kelly has a 28-11 record in three seasons with the Fighting Irish.
"I think from my perspective I've got the best job in the country, NFL, college, high school, whatever," Kelly said Saturday. "I just look at the place that I'm at and thankful for the opportunity that I have."
Just a year ago, Notre Dame athletic director Jack Swarbrick gave Kelly a two-year contract extension to keep him with the Fighting Irish through the 2016 season. Terms have not been released.
Kelly was hired in December 2009, getting a five-year deal. He left an undefeated Cincinnati team that was ranked No. 4 at the time. Fans liked his approach and his resume, which included improved records at Grand Valley State, Central Michigan and Cincinnati.
He has done the same thing in South Bend, begging the question of whether he is ready so soon to make a fresh move, this time to the NFL, or is perhaps trying to parlay a better contract out of Notre Dame.
Kelly was the third college coach Philadelphia has interviewed since firing Andy Reid on Dec. 31. Penn State's Bill O'Brien and Oregon's Chip Kelly interviewed with the Eagles last week, but chose to stay at their schools.
Philadelphia has interviewed six candidates and plans to meet with four others, but general manager Howie Roseman said Wednesday that the Eagles aren't in a rush to replace Reid.
Roseman, owner Jeffrey Lurie and president Don Smolenski also plan to meet with former Bears coach Lovie Smith on Thursday.
"Jeffrey has been very adamant with us that the key is getting the right guy," Roseman said in an interview on the team's website. "The key isn't getting the right guy as quickly as possible, so that's what we're going to do."
They met Denver offensive coordinator Mike McCoy on Sunday and plan to interview Indianapolis offensive coordinator Bruce Arians, Seattle defensive coordinator Gus Bradley and Cincinnati offensive coordinator Jay Gruden.
"This whole organization is built to support a head coach and they know that -- not only in actions but in words -- and all they have to do is call Andy Reid," Roseman said. "It's been a positive experience."
The interview with Chip Kelly last Saturday lasted for several hours, fueling speculation that he was going to take the job. But Kelly, who also was pursued by Cleveland, opted for the second straight year to pass up the NFL. He turned down Tampa Bay last year.
This is the third time Lurie is hiring a new coach since he bought the team from Norman Braman in 1994. He hired Ray Rhodes on Feb. 2, 1995, after a long, exhaustive search that included a flirtation with former Eagles coach Dick Vermeil. Lurie needed less time to hire Reid, giving him the job on Jan. 11, 1999.
ESPNChicago.com's Michael Wright and The Associated Press contributed to this report.