Adrian Peterson is scheduled to wrap up his free-agent visit with the New Orleans Saints on Tuesday. It’s unclear if that could materialize into an immediate contract offer or if the Saints just want to update their scouting report on a guy who hasn’t been available for a decade.

As I wrote when the visit was announced last week, running back has turned into a sneaky need for the Saints this offseason after they decided to let Tim Hightower get away to the San Francisco 49ers in free agency.

I would rank it No. 2 among their offensive needs heading into the draft -- behind only right tackle, where the Saints need to find an eventual successor for Zach Strief. Coach Sean Payton listed both positions among the team’s draft needs when he spoke at last month's NFL meetings.

Quarterback is more of a “want,” according to the Saints’ terminology. But since it’s such a vital position, that “want” could easily turn into a first- or second-round draft pick.

Here is a look at the Saints’ offensive depth chart as it stands after the first month of free agency.

QB: Drew Brees, Chase Daniel, Garrett Grayson

WR: Michael Thomas, Willie Snead, Ted Ginn Jr., Brandon Coleman, Tommylee Lewis, Jake Lampman, Corey Fuller, Jordan Williams-Lambert, Rashad Lawrence

RB: Mark Ingram, Travaris Cadet, Daniel Lasco, Marcus Murphy

FB: John Kuhn

TE: Coby Fleener, Josh Hill, Michael Hoomanawanui, John Phillips, Jake Stoneburner, Garrett Griffin

LT: Terron Armstead

LG: Andrus Peat, Senio Kelemete

C: Max Unger, Jack Allen

RG: Larry Warford, Landon Turner, John Fullington

RT: Zach Strief

K: Wil Lutz