Tom Coughlin waves to photographers as he leaves the New...

Tom Coughlin waves to photographers as he leaves the New York Giants training center in East Rutherford, N.J., Monday, Jan. 4, 2016. Credit: AP / Seth Wenig

During Tom Coughlin’s farewell media conference on Tuesday, he was asked how he might remain involved in the game. The former Giants coach reminded a packed audience inside the team’s training center that staying at home is not an option.

“My wife will not want me to be home longer than probably 48 hours,” Coughlin said. “ ‘There is your coat; don’t you have someplace to go?’ ”

As it turns out, that “some place to go” might be Philadelphia. Coughlin, who stepped down as Giants coach on Monday after a second straight 6-10 season, is scheduled to interview for the Eagles’ vacant head- coaching position tomorrow.

It remains uncertain whether Coughlin would accept the job — or whether the Eagles would offer it — but the chance to keep working in the NFL surely will be tempting for the 69-year-old. After all, the last time he was out of the game, he was miserable.

“He was like a fish out of water,” Judy Coughlin said a few weeks before Coughlin was hired as the Giants’ coach in 2004. “In one sense, it was good for him to see how the rest of the world lived. But there were days when he was like having a pet. He was never any trouble but always underfoot.”

Now Coughlin might have the opportunity to continue his career in Philadelphia, and Giants fans surely would wince at the notion of their former coach working for an NFC East rival.

Though Giants president and co-owner John Mara essentially decided that Coughlin had reached his expiration date after 12 seasons, Coughlin made it clear that he still has the energy to keep coaching.

When asked if he had extinguished his “coaching flame,” he replied on Tuesday, “Not necessarily. Not necessarily.” And if the right opportunity comes along . . . ? He interrupted before the question was finished. “I didn’t say that. I said I’m not necessarily done with coaching. Thank you very much for asking.”

The optics of Coughlin taking over in Philly certainly aren’t very good. Yes, he just went through a streak of four straight years in which the Giants failed to make the playoffs, the last three of which were losing seasons. But the Giants were competitive in all but two games this season, including one against the Eagles team he might coach.

You can make the argument that he did one of his better coaching jobs, because his roster was riddled with holes. The defense was one of the worst the Giants have fielded in decades.

Coughlin volunteered to step down, and he got no argument from Mara and fellow owner Steve Tisch. But rest assured he would have been back in 2016 if they had asked him to return.

Now Eagles owner Jeffrey Lurie will decide whether Coughlin can help restore his franchise’s credibility after Chip Kelly went scorched earth on the roster once Lurie gave him full personnel control. Coughlin surely would be welcomed by the Eagles’ demanding fan base, which has stood by helplessly while watching him win two championships. That’s two more than the Eagles have.

And if there is any question about whether Coughlin snubbed Mara as he walked off the stage at his news conference — it sure seemed awkward when Coughlin looked at Mara and then strode out of the room — taking the Eagles’ job would be the ultimate stiff-arm.

What are the Giants left with? Well, after seeing Coughlin go, they are left to hire from a flawed coaching class.

Former Bears and Broncos offensive coordinator Adam Gase interviewed with the Giants but took the Dolphins’ job. Giants coordinators Ben McAdoo, who has no head- coaching experience, and Steve Spagnuolo, who had a bad head- coaching experience in St. Louis, are on the list.

The Giants have interviewed former Bills head coach Doug Marrone, who earned mixed reviews in two seasons in Buffalo before quitting over a contract issue. On the same day Coughlin interviews in Philly, the Giants will talk to former Falcons coach Mike Smith, who finished 6-10 in his final season and has two fewer Lombardi Trophies than Coughlin. Mike Smith? Really?

It’s a bad look for a Giants team that usually is on top of managing its affairs. It doesn’t mean they won’t come away with a coach who ultimately will succeed, but for the moment, they look clumsy.

The idea that Coughlin could go to Philadelphia — and possibly take McAdoo if he doesn’t get the Giants’ gig and isn’t retained by whoever does — certainly wouldn’t sit well with fans.

Who else wouldn’t be happy? Eli Manning, who has adored working for both men.

But before we get ahead of ourselves, a word of caution for Coughlin: While he might be feeling jilted by the team he poured his life into the last dozen years, and while it might feel like the perfect in-your-face to coach against his old team, there is risk here.

Coughlin leaves the Giants with his reputation intact. He’s a potential Hall of Fame coach with two titles who did a terrific job with expansion Jacksonville, helped the Giants win a third Super Bowl as their 1990 receivers coach and had a superb run at Boston College. But the Eagles are a mess, and there isn’t a quarterback who comes close to Manning’s stature as one of the game’s top passers.

If Coughlin thought his Giants’ defense was bad, wait until he gets a look at the Eagles. They allowed 430 points — only 12 fewer than the Giants — and allowed at least 30 points in five of their last seven games.

With a successful rebuilding job, Coughlin’s stature would grow significantly. But anything less and he runs the chance of having his legacy tarnished.

For a scorned coach, it just might be worth the risk.