Dalglish, who had two spells in charge at Anfield along with an illustrious playing career with the Reds, has tipped Gerrard to be a contender to succeed Jurgen Klopp in the dugout when the German does depart.
He told BBC Sport: "For me it's not a shock he's done that well.
"I always thought he'd be a really good manager wherever he went.
"He took a big step to go to Rangers. He knew the size of the club and what it means to millions of people.
"He took a chance, he's a brave boy going there and it's worked out fantastically well for him.
"It's hypothetical, the job's not available.
"When it becomes available I'm sure Steven would be right up there in the contenders. He has done absolutely fantastic at Ibrox."