The 21-year-old is currently on a season-long loan from United to Tottenham.
Reports have suggested that Campbell could return to United in January, but the England Under-21 international says there is no recall option in his deal.
“I’m on a season-long loan and there is no break clause,” Campbell was quoted as saying in the Daily Star.
“The team’s playing good football and personally I’ve scored a few goals.
“I’m playing European football and I was more than happy to come to White Hart Lane.”
He continued: “I’d love to be the first homegrown striker to make it under Sir Alex at United.
“It can be difficult moving around. I would like to be settled somewhere.”