The Treasury is reviewing student loan repayment after a row over terms.
The government will publish clearer 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 reported £200bn mis-selling scandal.
The reported figure relates to claims that borrowers received inaccurate details on their loans.
No final decision has been announced.
The review is ongoing.