James has made 39 appearances in all competitions since joining from Swansea City, scoring four goals and registering six assists.
But the emergence of Mason Greenwood has relegated the Wales international to a substitute role.
Asked if there was any truth in the reports, James' agent Jonathan Barnett told Stretty News: "No. He's a major part of Man United's team. I see him playing for Man United."
Barnett added on James' character: "I think if you don't have that character you shouldn't go to Man United.
"We as a company have a responsibility to help them and point these things out and in Dan's case it was obvious he has that character.
"I think if you asked generally the people at Manchester United and I am presuming, I haven't spoken to them but they would be very pleased with his progress.
"It's very normal with a young player that he has a little dip in his form at the same time that the other guys have done extremely well, so he'll have to wait his chance and when he gets it, he'll take it."