Ronny Deila will leave Celtic at the end of the season.
Deila is in charge of Celtic at the moment, but the Norwegian will step down from his role at the Scottish Premiership giants at the end of the season.
Celtic legend Auld believes that the Bhoys should look at appointing O’Neill as their manager next season with Keane his assistant.
“Celtic should appoint Martin O’Neill, on the understanding that Roy Keane would come with him because you need that balance,” the former Scotland international told The Scottish Sun.
“And I’m telling you straight Dermot Desmond must unlock the purse. What we need is a strict person to come in.
“I think Keane is the right one because he won’t take any nonsense and having Martin back, he’d run things from the top of the house.”
O’Neill is in charge of the Republic of Ireland national football team at the moment, and former Manchester United midfielder Keane is the assistant manager.
The duo have done a great work so far and have guided the Republic of Ireland to the Euro 2016 finals this summer.
Both O’Neill and Keane have history with Celtic. While the former was the manager of the Hoops from 2000 to 2005, the latter ended his professional club football career at the Glasgow giants in 2006.
Celtic are at the top of the Scottish Premiership table at the moment with 77 points from 34 matches, nine points clear of second-placed Aberdeen.