Ryan Clark and Max Kellerman break down what the Saints' plan should be when pursuing free-agent RB Adrian Peterson. (1:45)

METAIRIE, La. -- Of course the New Orleans Saints' interest in Adrian Peterson makes sense.

No. 1: He's Adrian Peterson.

No. 2: The Saints have a bigger need at running back than many might realize after letting veteran backup Tim Hightower leave for the San Francisco 49ers.

I don't think the Saints should break the bank for Peterson, because they already have a very good running back (Mark Ingram), they still have bigger needs on defense and a younger running back in the draft would make more sense as a potential future successor to Ingram.

Adrian Peterson could provide the Saints with valuable depth alongside Mark Ingram. AP Photo/Andy Clayton-King

And maybe New Orleans' planned visit with Peterson next week is just one of those "due diligence" deals to find out where the 32-year-old is physically and what it might cost to sign him.

But it's smart business to check him out, considering Peterson is one of the greatest running backs in NFL history and led the league with 1,485 rushing yards in 2015 before a knee injury derailed his 2016 season.

NFL teams haven't gone overboard in trying to sign Peterson so far (though two pretty good ones -- the Patriots and Seahawks -- have brought him in for visits).

But if Peterson is healthy and available at a reasonable price, he certainly has the potential to be an upgrade over Hightower, whom I expected the Saints to re-sign after he played such a key role for them over the past two seasons. If re-signing Hightower seemed like a no-brainer, wouldn't Peterson be the same?

Hightower gained 923 rushing yards and 329 receiving yards and scored nine touchdowns over the past two seasons as a backup and fill-in starter -- including 100-yard rushing games in each season.

The Saints need someone else in that role, whether it's Peterson, another free agent or a significant draft choice.

Ingram is still just 27 and has been playing the best football of his career over the past three seasons. But running backs get dinged up, and the depth chart is extremely thin beyond him. Inexperienced second-year pro Daniel Lasco would probably be penciled in as Ingram's primary backup for now, since veteran Travaris Cadet is really more of a pass-catcher and kick returner.

Like I said, though, the draft probably makes even more sense than free agency to fill that void. Sean Payton has talked multiple times this offseason about how much he likes the running back depth in the middle rounds of this year's draft class.

I don't think the Saints should consider a running back in Round 1 -- even if LSU's Leonard Fournette somehow falls to them. I agree with what NOLA.com's Jeff Duncan wrote, that such a pairing would probably be a bit of a waste for both sides, since the Saints aren't a power-running team with Payton and quarterback Drew Brees, and running back is a part-time role in their offense.

Perhaps a dual-threat runner/receiver like Dalvin Cook or Christian McCaffrey would be even more tempting. But that would run counter to the Saints' decision to trade away a dynamic playmaker like Brandin Cooks for a first-round pick to add resources for the defense.

After that, however, a running back could make a lot of sense, maybe as early as Round 2 or with one of the Saints' two third-round picks -- even if they do wind up signing Peterson as a Hall of Fame stopgap.