The Premier League champions are considering whether to let the highly-rated England Under-20 international leave the club on loan in the coming weeks, as he is on the fringes of the first team.
Sky Sports understands there is interest from the Championship, whilst Cole has also attracted attention on the continent with German and Dutch clubs also showing an interest in landing the 20-year-old.
The player's agent Peter Morrison of James Grant Group has confirmed to Sky Sports that United are currently considering a number of approaches.
"I am aware that he has created quite a bit of interest and I'm not surprised given his performances last season," Morrison confirmed.
"Larnell is an exceptional talent but it is important that if he goes on loan it's to a club where he will not only play regularly but continue his development under the right manager as ultimately his aim is to play for Manchester United."
It is believed that David Moyes watched Cole on Monday evening when he scored one and made one as United lost 4-2 to Liverpool in the U21 Premier reserve league.