19-year-old Campbell has a prolific record of scoring goals and he proved that last season when he was loaned out to United's parent club Royal Antwerp.
The Huddersfield born striker netted 21 times in 33 appearances for the Belgium club as they finished 4th in the Belgium Second Division who are managed by Warren Joyce.
Crewe's technical director Dario Gradi told crewealex.net:"There is nothing in the pipeline regarding a striker. We asked Manchester United about Campbell but they are reluctant to let him go out on loan again.