Beale has been battling criticism since Rangers lost the Old Firm derby at home against a weakened Celtic side just ahead of the international break.
A timid exit from the Champions League and a slow start to the league season have doubled down the pressure on the Rangers boss.
He was allowed to overhaul the Rangers squad in the summer but none of his new signings have hit the ground running at the club.
Moore indicated that Beale is under severe pressure going into the game against St. Johnstone away from home on Saturday.
He is of the view that if Rangers drop any points this weekend, the Rangers manager will likely lose his job.
The former Rangers star said on the Go Radio Football Show: “If that [Rangers dropping points] happens this weekend, I can’t see at this moment in time with the swell that there is against him.
“If there are enough dropped points this weekend, I can’t imagine come Monday morning that Michael Beale would be at Rangers.”
Rangers are already trailing reigning champions Celtic by four points in the Scottish Premiership table.
