Johnson's future still remains unclear in the wake of England's disappointing World Cup campaign - with his current deal still to expire.
And Cooke, who led England to two grand slams during his seven years at the helm, wonders if Johnson will want to carry on after widespread criticism of the behaviour of his squad in New Zealand.
"I wouldn't be surprised if he decided he didn't want any more of it," Cooke told the Yorkshire Post. "He's got to ask himself does he need the flak that he's been getting."
If Johnson instead opts to carry on Cooke believes the Rugby Football Union will need to insist that he instigates a shake-up of his backroom team.
"I wouldn't be unhappy if they decided to stick with Martin Johnson; after all, he's got the experience now," he added. "But he certainly needs a different team of coaches with him.
"The key decision is still Martin Johnson. Everything depends on that, whether they decide to keep him on let him go or he decides to go himself."