Pro Football Talk's Mike Florio first reported the news Wednesday.
Stoops resigned from his post with the Oklahoma Sooners in June 2017. He spent 18 years in Norman, finishing with a 190-48 overall record. Under his watch, the Sooners were national champions in 2000 and won 10 Big 12 titles.
The XFL is set to launch in 2020 and announced the locations of its first eight teams in December: Arlington, Texas; Houston; Carson, California; East Rutherford, New Jersey; St. Louis; Seattle; Tampa, Florida; and Washington, D.C.
Stoops would be the first coach officially hired by the league.
According to Florio, the XFL will make the announcement Thursday, the timing of which was carefully planned.
The brand-new Alliance of American Football will get play started Saturday. By not only naming a new head coach but also one with Stoops' resume, the XFL can take some of the spotlight away from the AAF this week.
The fact the XFL would target Stoops, who said in October 2017 he didn't plan on returning to coaching, is a sign of the league's big ambitions.