The grass isn’t always greener, but in Tom Coughlin’s case, the uniforms could be.

Coughlin, head coach of the Giants until he “stepped down” from the position on Monday, is expected to meet with the NFC East rival Eagles about their head-coaching vacancy on Monday evening now that the Giants have given Philadelphia permission to talk to Coughlin.

The two sides are expected to have a feeling-out of each other at that time. The Eagles will measure how much desire Coughlin, 69, has to remain in coaching and Coughlin will gauge the immediate future of the organization.

It’s certainly not a done deal. But the possibility that a future Hall of Fame coach — a man so respected by the Giants’ franchise that they plan to induct him into their Ring of Honor during the 2016 season — could wind up facing the Giants twice a season looms large over the Giants’ own coaching search for a replacement for said fixture.

Still, the Giants are not standing in the way. Because Coughlin has one year remaining on his contract with the Giants, the Eagles needed to request permission for the interview. They did and it was granted.

Coughlin made it clear in his farewell address on Tuesday that his coaching flames have yet to be extinguished. It would take the right situation, of course, and the Eagles might fit some of his criteria.

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They play on the East Coast, which would allow Coughlin to remain close to his family, which includes 11 (soon to be 12) grandchildren. Coughlin also has a familiarity with the Eagles after preparing to play them twice a year the past 12 seasons.

While Philadelphia parted ways with Chip Kelly after only three seasons to create this opening, they previously had Andy Reid in place as head coach for 14 seasons, which speaks to stability.

Also, Coughlin’s NFL coaching career began as a wide receivers coach for the Eagles in 1984.

The Giants already have offered Coughlin a job in their organization in an as-yet-undetermined advisory role for personnel. Other teams have expressed interest in bringing Coughlin aboard in a similar position. The Eagles are the first to express an interest in him as a head coach.

It would not be unique for the Giants to have a two-time Super Bowl winner coaching elsewhere in the division. The Giants faced Bill Parcells when he was head coach of the Cowboys from 2003-06. In that case, though, Parcells was 13 years removed from his final season with the Giants. Coughlin hasn’t even been gone 13 days.

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Several years ago, it would have been almost unfathomable to think Coughlin could be the answer to a franchise that had just fired its coach and found itself looking for a replacement with a better “emotional intelligence.” That’s what Eagles owner Jeffrey Lurie said when he fired Kelly during Week 17 of the season.

But Coughlin’s passionate farewell speech on Tuesday — which displayed a clear bond with his players, references to loving each other, and comments that brought Eli Manning to tears — showed that Coughlin might have the element the Eagles are seeking.

As for his football resume, his two Super Bowl rings as a head coach put him well ahead of any other candidates in whom the Eagles have expressed interest. The Eagles already have interviewed Giants offensive coordinator Ben McAdoo, who also has interviewed for the Giants’ job.

Parcells, in fact, endorsed Coughlin for the Eagles’ job when he spoke on a Philadelphia radio station this past week.

“I know guys Tom Coughlin’s age who know a whole lot more about football than some of the 30-year-olds who are coaching it,” he told 97.5 The Fanatic on Thursday. “I think his record pretty much speaks for itself . . . The talent pool is a little bit thin right now.”

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If Coughlin does land the job in Philadelphia, he could bring McAdoo with him as offensive coordinator, possibly as head coach-in-waiting. McAdoo has one year left on his contract with the Giants, so they could block him from interviewing for anything below a full head- coaching job. However, if the new head coach of the Giants wants to bring in his own offensive coordinator and McAdoo is fired, he would be free to go anywhere he wants.