The 21-year-old still has four years remaining on his contract at St Mary's, but the Saints have indicated that they are happy for the attacker to continue his development in the Championship.
Wolverhampton Wanderers have been strongly linked with the former England Under-20 international, but Bruce has revealed that he has identified Gallagher as a potential target ahead of the end of the transfer window.
The 56-year-old is quoted by the Express & Star as saying: "Every club in the Championship has been linked with him. It's something we're looking at us. He interests us yes."
Last season, Gallagher netted 11 goals in 43 Championship appearances during a loan spell with Blackburn Rovers.