The 20-year-old prospect joined Leeds in 2019 from Carlisle United.
The Scottish winger has made three appearances in the Premier League 2 for Leeds United's U23, scoring one goal.
Galloway made the trip across the Pennines and featured in FC United's 3-4 defeat to Whitby Town on Tuesday.
FC United will travel to Lincolnshire at the weekend as they face-off against Grantham Town, who sit at the bottom of the Premier Division.
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