Magpies boss McClaren is a huge admirer of the 22-year-old midfielder and took him on loan at Derby last season.
Lingard signed a new deal at Old Trafford in February, but has been unable to force his way into the first-team reckoning and despite his insistence that he wants to stay, could be forced to look elsewhere for regular football.
On Tuesday, The Sun claimed the player was the subject of a potential £2.5million bid from Bristol City but reports now suggest the player is wanted by McClaren at Newcastle.
Lingard recently emphasised his desire to stay and fight for his place at his boyhood side.
He said: “The manager has not said anything to me at the moment regarding my future.
“This is my club. This is where I want to stay.”
Lingard has also spent loan spells with Leicester, Birmingham and Brighton.