The Treasury is conducting a review of student loan repayment after a row over terms.
The government will publish clearer guidance on repayments in England.
The review follows a dispute over loan conditions and repayment obligations.
Burnham has resisted Budget reforms.
Labour has left the door open to 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.