Sir Keir and Ms Long-Bailey are viewed as the two front runners in the battle to succeed Jeremy Corbyn at the head of the party, with the shadow business secretary favoured by influential voices on the left like shadow chancellor John McDonnell and the leaders of the Momentum movement.
Sir Keir has signalled he will seek to unify Labour and drive out factionalism if he takes the helm, fuelling expectations he will appoint a senior team drawn from all wings of the party, including Corbyn loyalists like Ms Long-Bailey.
But one MP who nominated the shadow Brexit secretary told The Independent that the drive for unity may not stretch to putting Ms Long-Bailey into the party’s second most powerful position of shadow chancellor.
The MP stressed he had not been given any guidance from Sir Keir on his appointment plans, but added: “I don’t think he’ll make Becky shadow chancellor. She doesn’t have a lot of experience.”
Sir Keir could be expected to offer jobs to leading figures from the left, including Ms Long-Bailey, shadow justice secretary Richard Burgon – currently running for deputy leader – and up-and-coming international development spokesman Dan Carden, the MP suggested.
“I think there’d be a place for people like Becky, and even Richard Burgon would be given something low profile which didn’t involve him being on the media too much,” the MP said.
“The key thing, really, is that there’s a lot of people in the parliamentary Labour party with a lot of talent who need to be brought on, and they come from right across the spectrum, from Wes Streeting in the centre to Dan Carden on the left, and I think he’ll want to make use of that range of talent.”
The MP said that Corbynites were not expected to be “obstructionist” and retreat to the backbenches if their candidate lost, and said: “I think they’d be ready to serve on the front bench under someone like Keir.
“The left have suffered a real blow to morale from the election, they’re more fractured and they’re not going into this leadership battle with the same unity behind a candidate as they did in 2015 or 2016.”
Sir Keir has yet to give any public indication of who he will appoint to his shadow cabinet if he wins.