Alex McLeish stressed the need for Rangers “to get off to a flier” next season while Celtic reset following the departure of Ange Postecoglou.
The dominant Hoops claimed the domestic treble last season but are searching for a new boss after the former Australia manager left last week to join Tottenham.
Rangers manager Michael Beale is continuing the revamp of his squad with the recruitment of midfielder Kieran Dowell from Norwich, defender Dujon Sterling completing a move from Chelsea and goalkeeper Jack Butland joining after his release from Crystal Palace, with the promise of more to come.
McLeish, boss at Ibrox between 2001 and 2006, offered some advice to his former club, saying: “They have to make a great start.
“While Celtic may be with a new manager, new coaches, planning a strategy maybe not the same as Postecoglou’s, there could be a little bit of disruption and Rangers have to start extremely well.
“The big thing is recruitment.
“I am sure Michael has a good eye for players and if he has the right signings…they have to get off to a flier.
“I’m sure he has brought young and vibrant players in but when you come to a club like Rangers you’ve got to hit the ground running and that’s just the facts.”