But Mrs Shephard retorted: "Stuff and nonsense! Delegated budgets are popular with schools, and there have been no suggestions that schools want to return to the previous arrangements."
She praised local education authorities for getting LMS schemes into place, and said heads and governing bodies had done a "remarkable job".
Mrs Shephard pledged that GM schools would continue to receive resources to match their additional responsibilities - either through LMS replication or the Common Funding Formula (CFF) which is being piloted in five authorities.
She added: "It is clear that GM schools in other areas - including primary schools - would also like to see the CFF replace LMS replication at the earliest opportunity.
"I am not going to be rushed into headlong expansion. But those who advocate standing still are going to be disappointed."