O'Neill is among the name being tipped to replace Pedro Caixinha at Rangers, three weeks since the Portuguese left Ibrox.
O'Neill, who is reportedly interesting Scotland and Sunderland too, could leave his position as Northern Ireland boss after their World Cup play-off defeat against Switzerland.
But Brazil, an open follower of Rangers' Glasgow rivals Celtic, insists the 48-year-old should not be considered by the Ibrox powers-that-be.
Discussing the latest odds on O'Neill's future, the Talksport host said on Thursday's Sports Breakfast show: "He can’t do the Rangers job - strike him off your list.
"You cannot go from Shamrock Rovers to Rangers."
It is unclear however, whether Brazil's issue lies with O'Neill's lack of club management experience outside of Ireland, or the affiliation between Shamrock and Celtic, who share the same colours (green and white) and nickname (the Hoops), among other similarities.
Whatever his reasoning, Brazil's view is not shared by co-host Ally McCoist, the former Rangers player and manager, who added: "Course you can!"
O'Neill is under contract with Northern Ireland until 2020, meaning Rangers would have to pay a fee if they wish to appoint him as Pedro Caixinha's successor.
Should Rangers consider O'Neill?