An announcement is expected sometime this week.
McLellan coached the San Jose Sharks for the last seven seasons, but became available when he mutually agreed to part ways with the team in April.
The 47-year-old also coached Canada to a gold medal at the world championship which wrapped up in the Czech Republic on Sunday.
McLellan compiled a 311-163-66 regular-season record with the Sharks, but failed to guide the team to a playoff appearance this season.
In Edmonton, he will have a chance to coach Connor McDavid who is expected to be selected by the Oilers with the first pick in the draft next month.
The Oilers will reportedly surrender a third-round pick if the deal to hire McLellan is completed.