Multiple published reports say that while a deal has not yet been finalized, the Oilers are expected to announce the hiring sometime this week.
McLellan coached the San Jose Sharks for the last seven seasons before parting ways with the team after missing the playoffs this April. The 47-year-old was 311-163-66 with the Sharks.
McLellan also coached the Canadian men's hockey team that won gold at the world hockey championship in Prague on Sunday. It was Canada's first gold medal at the tournament since 2007.
Edmonton has not had a full-time head coach since the team fired Dallas Eakins last December. Todd Nelson filled in as an interim coach for the rest of the 2014-2015 season.