According to Dan Wolken of USA Today, several college athletics insiders believe Stoops "would be in a class by himself as a candidate" for the head coaching job at OSU.
Ohio State placed Meyer on administrative leave Wednesday to investigate whether he knew about domestic violence allegations against former wide receivers coach Zach Smith in 2015.
Smith's ex-wife, Courtney Smith, told Brett McMurphy that she had conversations with Meyer's wife regarding the alleged abuse.
In one of those conversations, Shelley Meyer reportedly suggested she was going to notify her husband: "Shelley said she was going to have to tell Urban. I said, 'That's fine. You should tell Urban.' I know Shelley did everything she could."
Courtney Smith isn't certain Urban Meyer knew about the situation, but she told Stadium that she believes he had some knowledge: "I do believe he knew, and instead he chose to help the abuser and enable the abuser and believe whatever story Zach was telling everybody."
At Big Ten Media Days in July, Meyer said he previously had no idea about the 2015 allegations, per McMurphy: "I was never told about anything. Never anything came to light, never had a conversation about it. So I know nothing about it. I asked people back at the office to call and see what happened, and they came back and said they know nothing."
Meyer fired Zach Smith last month after he was arrested for criminal trespassing on his ex-wife's property.
If Ohio State moves on from Meyer, Stoops appears to be an ideal replacement due to his experience at the highest level of college football.
Stoops, 57, coached the Sooners for 18 seasons from 1999 to 2016 before retiring prior to the 2017 campaign.
He had an overall record of 190-48 and won at least 10 games in all but four of the seasons he spent at Oklahoma.
While it is possible the 2000 national champion could come out of retirement, Wolken noted that those close to him believe he is done coaching.
If Ohio State does land Stoops, it would be hiring one of the top college football coaches of the past two decades. He's a one-time Associated Press Coach of the Year, two-time Walter Camp Coach of the Year and six-time Big 12 Coach of the Year.