The 18-year-old will get his first taste of regular senior football away from United after agreeing the move to the north-west club, who are embarking on a promotion push in League One.
Ian Evatt's side are currently fifth in the division and are away to another big club, in Derby County, on Saturday afternoon.
Shoretire played against the Trotters in the Papa Johns Trophy recently, as the young Reds were knocked out of the competition at the University of Bolton Stadium.
The 2020/21 Jimmy Murphy Young Player of the Year scored in the game with Fleetwood Town, earlier in the competition, and also found the net in the Premier League 2 victory at Fulham on 6 January.