The 22-year-old had a difficult 2016-17 campaign at United after struggling to overcome the physical and mental pain that was caused by his double leg break in September 2015.
Shaw, who only started nine Premier League matches last season, is closing in on a return to fitness after missing the end of last season with ankle ligament damage.
It has recently been claimed that the England international could be used by United in an attempt to sign Tottenham Hotspur's Danny Rose this summer, but according to Shaw's agent, the left-back will not be leaving Old Trafford.
"Luke Shaw is going to be one of the best left-backs in the world. Manchester United love him and Luke Shaw loves Manchester United," Barnett told the International Business Times.
The Red Devils will open their 2017-18 Premier League campaign at home to West Ham United on Sunday afternoon.