Labour MPs are circulating a letter seeking to overturn the decision.
The letter to Sir Keir, which is being circulated by the Left-wing MP Clive Lewis, urges the full NEC to “re-evaluate” its decision and let the local party in Gorton and Denton decide whether Mr Burnham should be the candidate.
The letter warned that losing the by-election would be “unimaginable... blocking him from even making his case to local members risks sending a message that the party does not respect devolution”.
It added: “It risks telling our own local members that we do not trust them to make the important decision on who is best placed to fight this election for them and serve as the next MP. Fundamentally it risks playing into the kind of division and disunity that Nigel Farage and Reform thrive on.”
John McDonnell, the former shadow chancellor under Jeremy Corbyn, said the NEC – as the governing body of the party – had the authority to overrule the panel that blocked Mr Burnham.
Earlier, he had posted on X: “Message to Keir: Do not underestimate the depth of anger people will feel about this disgusting decision.
“If you think it strengthens you I tell you it will simply hasten your demise. You could have shown magnanimous leadership but instead it’s cowardice.”