Earlier in the day, Andy Burnham, the UK Shadow Health Secretary and a candidate for leading the Labour party, urged Miliband to intervene to persuade the Labour Party faithful not to become "a powerless party of opposition" by electing Corbyn, the current front-runner, leader.
"Ed [Miliband] will not be intervening in this contest as he has said right from the start. He is following established precedent and believes that the debate must play out between the candidates," the spokesman said, as quoted by The Telegraph newspaper.
Opponents argue that Corbyn’s leadership would lead to a Labour defeat in the next UK general election, due to be held in 2020.
The Labour leadership vote was triggered by the resignation of leader Ed Miliband following his party's decisive loss in the May general election.
Voting in the Labour leadership contest will conclude on September 10. The results are expected to be announced two days later.