But we've come up with a shortlist of 10 from the first team, Under-21s and Under-18s, and we want you to pick your favourite. Vote via our online competition and you could win a shirt signed by the winning player (terms and conditions apply).
Our video of the contenders features Robin van Persie's goals against Cluj and Chelsea, plus contributions from Tom Cleverley, Danny Welbeck and Nani.
Three Under-21s goals – scored by Larnell Cole, Frederic Veseli and Tom Lawrence – are up for the award, while the Under-18s are represented by Andreas Pereira and James Wilson.
Vote here for United's Goal of the Month. Good luck!