His comments came in response to calls for a return to Labour ministers electing the top jobs, which was standard procedure before Ed Miliband abolished the tradition in 2011, prefering to make his own appointments.
Speaking at the weekly meeting of the Parliamentary Labour Party (PLP) on Monday, a spokesman for the Labour leader said MPs should consider letting party members elect some Shadow Cabinet positions.
The spokesman added that any move to return to annual shadow cabinet elections should be “part of the wider debate about party democratisation and reform."
Clive Betts, Labour MP for Sheffield South East, tabled the motion to return to the old system for debate at the PLP meeting.
Mr Miliband originally persuaded MPs to vote against elections for Shadow Cabinet ministers to allow the party leader freedom to choose their own Cabinet. He said at the time that Shadow Cabinet elections were a "huge distraction" and he wanted Labour to "spend our time talking to the public and not ourselves."
The motion is being presented by Mr Betts and his supporters as a way of repairing damage done to the party by the current leadership contest, which Mr Corbyn is expected to win.
Mr Betts said in an email before the debate that he wanted to promote party unity.
“Whatever the result of the leadership election on 24 September, it is clear that the PLP must take steps to come together," he said.
"[Holding further elections] would ensure that the Shadow Cabinet has the support of backbench Labour MPs and that the entire PLP can become an effective opposition and hold the government to account.”
But Corbyn supporters believe the move is intended to undermine the Labour leader, who has strong support from party members but is unpopular with the PLP. A Shadow Cabinet elected by MPs would be unlikely to support him, which could limit his power and allow the right of the party to maintain control.
Leadership challenger Owen Smith told BBC News on Sunday that he believed bringing back Shadow Cabinet elections in which ministers could participate was “probably a good idea” and that “getting rid of them was a mistake.”
He agreed that it could be a useful means to unite the party.
A few hours later Mr Corbyn's spokesman appeared to up the ante, saying that the Labour leader also wanted more internal democracy, but that he was interested in going further.
“Jeremy supports democratisation and reform of the party rules and structures,” the spokesman said.
“How the Shadow Cabinet is made up is one part of that debate, including whether part of it should be elected, by MPs, by members, or by conference. Any review also needs to take account of the need to represent regions and nations.”
Labour MPs are expected to hold a formal ballot on Mr Betts' proposal.
In 2011, Labour MPs backed Mr Miliband’s proposal to revoke the PLP's right to select the Shadow Cabinet by 196 votes to 41.
Considering how unpopular Mr Corbyn is with the PLP, it is likely they will vote to reverse the decision. However, for the new rule to take effect it would also have to be approved by the national executive committtee (NEC), where Mr Corbyn has more support, and by the party conference.
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