Cole, 27, supported the US group during the European leg of their last tour after becoming good friends with band member Will.i.am.
According to UK newspaper Daily Mirror, Fergie said: 'She is such a good friend. But I don't think she has quite got her head around how big she is going to be.
'My girl really can rule the world. I have already heard crazy things like Robert De Niro wants to make movies with her and that Jay-Z wants to work with her.
'Within five years we could be talking about Cheryl on the same level as we do Madonna or Mariah Carey.'