Further pressure has been piled on Cook's shoulders in recent weeks following the 3-1 defeat to India, but the England skipper has repeatedly insisted that he has no intention of resigning as the team prepare for the tournament, which will be held in Australia and New Zealand early next year.
"I think he's the man to lead the side forward," Grayson told BBC Essex. "I know he wanted to lead the one-day side to the World Cup, and maybe he will assess it then and think it's time to just go back and do the Test side.
"They've taken it so far now, with the World Cup around the corner they would be stupid to lose Alastair as captain now.
"He's trying to lay the foundations for that big competition which is less than six months away."
Cook is currently taking a break from cricket after the ECB confirmed that he would not be available for Essex's three remaining County Championship fixtures.