Stewart, 25, enjoyed a prolific 2021-22 campaign in front of goal, scoring 26 times in 53 appearances across all competitions, and he helped the Black Cats secure promotion to the Championship via the playoffs.
The former Ross County man joined Sunderland in January 2021, but he only has a year remaining on his contract at the Stadium of Light.
According to the Northern Echo, Giovanni van Bronckhorst regards Stewart as his primary target, but Rangers will only plan to make a move for the Scotsman if their current first-choice striker Morelos leaves the club this summer.
Morelos is an invaluable asset for the Gers, but his long-term future at Ibrox is uncertain as he will soon be entering the final year of his contract.
The report adds that Rangers will not risk losing the 25-year-old Colombian for free in the summer of 2023 and will therefore look to sell the striker if he decides against extending his contract.
Morelos, who has previously been linked with Premier League trio Aston Villa, Leicester City and Newcastle United, has recorded 113 goals and 51 assists in 224 appearances for Rangers since joining the club in 2017.