Hall of Fame boxing promoter Bob Arum once famously said, “Yesterday I was lying. Today I’m telling the truth.” It was uttered nearly 40 years ago during a debate over drinks as to who the top fighters were of the day.

Arum, 84, is in Las Vegas promoting a pay-per-view bout Saturday night featuring Manny Pacquiao. But he swears he is telling the truth about Alabama coach Nick Saban having interest in being the head coach of the Giants before the organization hired Ben McAdoo last summer.

Arum confirmed a report on NorthJersey.com saying he was the one who put Saban’s representatives in touch with the Giants. Arum told The Post it started with a call from Nick Khan, an agent at CAA who has a colleague who represents Nick Saban. Arum was contacted because of his friendship with Giants co-owner Steve Tisch.

“I called Steve Tisch up,” Arum told The Post on Friday. “He talked to [John] Mara, but they had to act quickly. CAA was already looking for homes in New Jersey. Then Saban’s wife said they didn’t want to leave Alabama.

“They did it all on a confidential basis,” Arum added. “I can’t say I’m part of this thing. I was just called upon to perform that one task.”

Had Saban’s wife, Terry, agreed to come to New York, Saban could be the head coach of the Giants today. Instead, McAdoo takes a 4-3 record into Sunday’s critical NFC East game against the Eagles at MetLife Stadium.

The Giants have denied having interest in Saban, but that’s what everyone says when things don’t work out. Still, it’s interesting to know there were at least admiring glances exchanged before Saban’s wife decided not to let things get too far.

The jury is still out on McAdoo and whether he will be a successful head coach in the NFL. It makes sense the Giants might revisit their conversations with Saban if McAdoo’s rookie season somehow implodes.

Sunday’s game will be a critical test of McAdoo’s coaching ability. How will his team respond coming off a bye week? How will it respond after the Josh Brown distraction? Can it put together a string of four-quarter performances? Can the Giants get on one of those late-season tears that have led to Super Bowl triumphs?

The midpoint of the season sees the Giants trying to stay within arm’s length of the division-leading Cowboys (6-1), while the Eagles and Washington are also 4-3. McAdoo’s toughest Sundays are still ahead and a fan base can turn quickly if it thinks someone as high-profile as Saban might be available.

Arum, a lifelong Giants fan, said he was excited initially to learn of Saban’s interest.

“I really believe that two of the best coaches in college ball are [Jim] Harbaugh at Michigan and Saban of Alabama, and I think Saban might be the best football coach in the country,” Arum said.

But he likes McAdoo, too.

“They made the choice of McAdoo and let’s see how McAdoo does,” Arum said before launching into his disgust the Giants don’t have a quality tight end on the roster. “At the Super Bowl I told Steve Tisch the only way the Giants will be a Super Bowl team is if they get a world-class tight end. Meanwhile, they have no one. Larry Donnell can’t block me.”

Saban’s wife probably did the Giants a favor. Saban might have been too hard to pass up if he wanted to succeed Tom Coughlin. But at age 65, Saban’s stern approach might not work in today’s NFL any better than it did when he coached the Dolphins to a 15-17 record over two seasons (2005-06). Then again, Saban might to be looking for a Super Bowl trophy to complete his coaching career.

McAdoo, hungry and driven at age 39, at least has the chance to grow into the job the way Bill Parcells did. We’ll see how he’s doing on Sunday.