John McDonnell has suggested a compromise may be reached on an attempt by Jeremy Corbyn's allies to make it easier to get a candidate from their wing of the party into a future Labour leadership contest.
The shadow chancellor said "the heat is off" on the so-called "McDonnell amendment", which would allow candidates to stand for the leadership with the support of fewer MPs, and ruled out standing for the position himself.
Some observers had predicted a battle over the amendment - which would lower the threshold required to get on the leadership ballot from 15% of MPs to 5% - at next month's party conference.
But Mr McDonnell said the mood towards the left wing of the party had changed among MPs after Mr Corbyn greatly outperformed expectations in the General Election.
Critics had believed allies of Mr Corbyn wanted to pass the amendment at the Brighton conference in September to tighten their grip on the party, with a left-wing candidate more likely to be supported by members, who are given a vote only after candidates are nominated by MPs.
But Mr McDonnell told the Guardian: "For propaganda purposes people are calling it the McDonnell amendment, but I've distanced myself from it all along: one, I'm never standing for leader of the Labour party, and two, it wasn't my idea in the first place.
"I think there's a demand for change in terms of the nomination procedure, and in the usual Labour Party way, if it does get pushed by some, there will be a compromise around what's liveable.
"But the heat is off really; it's not as critical for some people as it was in the past."
He added: "The nature of the PLP (parliamentary Labour party) has changed, so there's less of a sense of urgency in that sense.
"The atmosphere's changed; people are thinking it's better to have a range of candidates if there's a change of leadership at some time in the future, and what's wrong with that?"
On Saturday, Mr Corbyn was continuing his summer tour of marginal constituencies with visits to Conservative-held Aberconwy and Plaid Cymru-held Arfon in north Wales.
Aberconwy is held by Tory Guto Bebb with a slim majority of 635 votes, while Plaid's Hywel Williams holds Arfon with an even tighter lead of 92 votes.
Ahead of the visits, Mr Corbyn said: "We can win here and form the next government that will work for the many not the few."