The Dons lost youngster Jack Grimmer to Fulham in January and Fraser Fyvie has confirmed his intention to leave.
Aberdeen are now aware that left-back Robertson is attracting interest after making the breakthrough into the first-team over the past year.
The 18-year-old left-back is a Scotland youth international and very highly-rated.
The Dons are hoping that he can be persuaded to commit his future to the club.