The 38-year-old made nine appearances in the Premier League last season as West Brom were relegated from the top flight of English football.
Contact has been made with the player’s representatives about the possibility of him signing a one-year deal to move north of the border. A number of Championship clubs are also said to be interested in the centre-back.
Gerrard has made the position one of his top priorities since agreeing to become the next manager at Ibrox, with a move for Brighton defender Connor Goldson also in the works.
McAuley has made 79 appearances for his country. He famously scored the first goal in a Euro 2016 victory over Ukraine, a result which heavily contributed to Michael O’Neill’s side reaching the knockout stages.