Brown has recently been playing in the first team due to the injury to Paul Robinson and the 27 year old is said to have impressed Boro manager Gordon Strachan.
The Boro boss does have the likes of Brad Jones and Danny Coyne available in his squad, but it is rumoured he has his sights set on Brown to bolster his squad.
Should Brown be interested in a move he could buy himself out of his current contract under the Webster Ruling.