Mrs Hodge faced tough questions from MPs this week on how she would ensure schools shared out vulnerable children fairly.
Members of the Commons education select committee told her the Government's plan to make schools more independent was at odds with its drive to get them working in partnership.
Asked whether one solution would be to give schools extra money as an incentive to admit vulnerable pupils, Mrs Hodge replied: "Yes, it could be."
She said she expected up to 10 per cent of local authorities to have problems encouraging schools and other agencies to work to support young people.
But the planned database containing details of all pupils would cost "in the low hundreds of millions" rather than the billion pounds some had estimated, said Mrs Hodge.
Committee chairman Barry Sheerman said he was sceptical about the minister's claims that the implementation of the Children Act would not require a vast increase in funding.