The war bond proposal was rejected earlier in June by outgoing Prime Minister Keir Starmer, who described war bonds as "just another type of loan".
But one of Andy Burnham's most important advisers, the Bank of England's former chief economist Andy Haldane, has previously spoken positively about the proposal.
British war bonds - which were issued in large series during the First and Second World Wars - would be earmarked for defence spending and could have special conditions, such as exemptions from inheritance and profits tax for lenders.
The British opposition party, the Liberal Democrats, has repeatedly called for the issuance of war bonds.
