Dack played under Mowbray at Blackburn between 2017 and 2022 and the now Sunderland boss remains a firm admirer.
Now Dack is a free agent following his release from Blackburn and is looking for a new club at which to continue his career.
Mowbray wants him at Sunderland, but will need to come up with a convincing offer to tempt Dack to the north east.
The Championship club have so far focused on getting young players matching their budget.
However, Sunderland could go against their policy to sign Dack if an agreement on personal terms can be reached.
The Black Cats have so far signed four players, two of them aged 20 while the others, Jobe Bellingham and Luis Semedo, are 17 and 19, respectively.
Dack, on the other hand, could provide Sunderland with valuable Championship experience having played 116 matches in the division and having making 42 goal contributions.
