Mr Burnham warned that without a major shift in direction, Sir Keir risks allowing Nigel Farage's Reform party to gain power.
His intervention comes amidst Labour's struggles in opinion polls and growing questions among MPs about Sir Keir's leadership, particularly if upcoming elections are poor.
Mr Burnham's message, which includes criticism of welfare cuts, is expected to resonate with delegates at the crucial Labour conference.
Supporters are positioning Mr Burnham as a potential future leader, with allies like Lucy Powell and other rebel MPs aligning with him against the current leadership.