The Treasury is conducting a review of student loan repayment after a row over terms.
The government will publish more straightforward guidance on repayments in England.
The review follows a disagreement about loan conditions and repayment obligations.
Burnham has opposed Budget reforms.
Labour has not ruled out a reversal on repayments after a widely reported £200bn mis-selling scandal.
The reported figure comes from claims that borrowers received inaccurate details on their borrowing.
No final decision has been announced.
The review is ongoing.