Dalglish has been tasked with finding a successor to Benitez, who left by mutual consent, alongside managing director Christian Purslow.
But the Scot - the last Liverpool manager to deliver a league title to Anfield in 1990 - is among the bookmakers' favourites for the job.
And Grobbelaar believes Dalglish could be the stabilising influence Liverpool now require.
"I think there is only one man for the job and that is Kenny Dalglish," Grobbelaar told BBC Radio Five Live.
"I believe if he didn't have the appetite for the game, he wouldn't be at Anfield every week, week-in, week-out.
"I think maybe now is the time he can turn the tide and take the club, stabilise it, with the fans, make sure everything gets on track and take the club where it should be.
"We were in seventh position last season, this season he's got to stabilise it and put it back on track."
Dalglish was installed as player-boss in 1985 and delivered three league titles and two FA Cup triumphs.
He also presided over a difficult period surrounding the Hillsborough disaster, the emotional toll of which contributed to his departure in 1991.
Grobbelaar believes Dalglish has the kudos required to take the role once more.
"As a manager he'll be respected and if fresh players come in, he'll be able to lead them," added Grobbelaar.