The Treasury is reviewing student loan repayment after a row over terms.
The government will issue more straightforward guidance on repayments in England.
The review follows a dispute over loan conditions and repayment obligations.
Burnham has opposed Budget reforms.
Labour has left the door open to a reversal on repayments after a widely reported £200bn mis-selling scandal.
The reported figure relates to claims that borrowers received inaccurate details on their borrowing.
No final decision has been announced.
The review is ongoing.