Current leader Ed Miliband is expected to step down after his leadership presided over the party losing over 20 seats and all but wiped out long-standing Scottish support in the 2015 election.
Mr Burnham has odds of 2/1 to win with a host of online bookies. Yvette Cooper and Chuka Umunna are other strong contenders for Labour leadership.
He retained his seat in Leigh with a 14,000-vote lead over the Tory candidate, Louisa Townson, winning an overall 24,312 votes.
Party leaders resign
It has been widely reported that Mr Miliband is expected to resign later today. Liberal Democrat leader Nick Clegg and UKIP leader Nigel Farage have already stepped down in the wake of Thursday's election.
Mr Miliband took to Twitter to say: ‘This has clearly been a very disappointing and difficult night for the Labour party. To every member and supporter, I want to say thank you.
‘I am grateful to the people who worked on our campaign and for the campaign they ran. The responsibility for the result is mine alone.’
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