McNair was promoted from the reserves by Louis van Gaal at the beginning of last season but was widely expected to have a peripheral role at Man United.
However, the 20-year-old put in some match-winning performances for the team and at times became a valuable part of the starting XI.
Despite this, Bruce is hoping van Gaal will let McNair leave on loan in a move that would see the young Northern Irish international replace James Chester, who has recently moved to West Bromwich Albion.
With United almost certain to experience an injury crisis at some point, many fans feel it would be unwise to let McNair leave without adequate cover.
The centre-back’s performances belied his years last term, and with deals for Sergio Ramos and Nicolas Otamendi looking increasingly uncertain, McNair might be poised for more first-team action this season.
However, it is understandable why Bruce has his eyes set on McNair. The 20-year-old showed last year that he has the quality to become a fine player, and for a Hull side looking for immediate promotion from the Championship, it is not surprising that he is a wanted man.