Gerrard is 18 months into his first management role at Ibrox after a stellar playing career with Liverpool and England.
He led the Scottish Premiership side to second place last term – their highest finish since 2016 – and the Europa League group stage.
“Coming to Scotland has been a fantastic move for him,” said Elliott.
“He was a great player and I always believed he would have a natural progression into management. There was just something about him, he’s different, he thinks different.
“He’s a natural leader and management is in his DNA. I actually think he’s a long-term future England manager, potentially. I rate him that highly.”
Elliott joined Celtic for a two-year spell in 1989 when Rangers had won the first of their nine successive titles.
Neil Lennon is attempting to match that title feat with Celtic this term and Elliott says an away victory in Sunday’s Old Firm game at Ibrox on Sunday could “destabilise” Rangers.
“I want Neil to do well,” the 55-year-old added. “He has been a terrific manager for the club.