Beale was sacked on Sunday night following Rangers’ 3-1 defeat at home to Aberdeen, which left his position at Ibrox untenable.
Rangers are now in the market for a new manager and are expected to finalise an appointment during the international break.
Former Rangers left-back Kevin Muscat is open to discussing becoming the next manager at Ibrox and the club have also made enquiries for Preston North End boss Ryan Lowe.
Ferguson stressed that Rangers need to be careful with the next appointment as they badly need some stability and someone who will be at Ibrox for a few years.
He pointed out that the managerial churn over the last few years has not been in keeping with the club’s history.
The Rangers legend said on the Go Radio Football Show: “They have got to be careful in making sure that it’s the right guy.
“That’s seven managers they have had in the past five years and if you look back in Rangers’ history, it has not been like that.
“So, they need to get somebody in who is going to steady the ship and be here for the long haul for the next three, four or five years.”
Steven Davis has been placed in interim charge of the Rangers side as the club look for a new manager.