Dave Tippett could succeed Ken Hitchcock in Edmonton.
TSN's Pierre LeBrun later backed up Rishaug's report, adding that Tippett "still figures prominently" in Edmonton's search.
The former Arizona Coyotes head coach has been a senior advisor with the Seattle-based expansion franchise since last June.
Tippett reportedly interviewed for the Buffalo Sabres' head coaching position before they hired Ralph Krueger.
Oilers general manager Ken Holland revealed at his introductory news conference on May 7 that Hitchcock wouldn't be back next season.