Reidford, 20, is fourth choice behind Alan McGregor, Neil Alexander and Graeme Smith at the Glasgow club and has decided he needs regular first-team football.
"I've been here a long time, but I'm no closer to getting in the first-team.
"It's hard, but when you look at the guys in front of me, you can understand why it's not happening for me.
"I'm 20 and I think I'm at the age now when I need to be playing football."
League One side Oldham are understood to be interested in the youngster.