Burnham, one of the party's most high-profile politicians and an elected mayor in the northern English city of Manchester, said on Saturday he wanted to become Labour's candidate to replace an MP who resigned last week.
Local news outlets reported that he was refused permission by Labour's National Executive Committee.
Blocking Burnham's candidacy will deny him the chance of winning a platform from which he could have formally challenged Starmer, because only members of parliament can trigger a leadership contest.
The decision was made by a 10-strong sub-group of the NEC, chaired by the Home Secretary Shabana Mahmood on Sunday morning.
Confirming the decision in a statement, the Labour Party said the NEC had decided to deny Burnham permission to stand in order to avoid "an unnecessary election for the position of Greater Manchester mayor".
The party said a mayoral by-election "would have a substantial and disproportionate impact on party campaign resources" before local elections in May.
"We believe it is in the best interests of the party to avoid an unnecessary mayoral election which would use substantial amounts of taxpayers' money and resources that are better spent tackling the cost of living crisis."
The NEC decision will fuel discontent in a governing party whose popularity has plummeted since a landslide election win in July 2024 as Starmer has struggled to deliver on promises of a stronger economy, better public services and tighter borders.
Last week, bond markets reacted negatively to the prospect of Burnham's return to parliament, with some investors taking a view that it could trigger political turmoil and, if he did eventually replace Starmer, a looser fiscal policy.
Burnham criticised Starmer's leadership last year but said on Saturday he had assured the prime minister he wanted to "support the work of the government, not undermine it".
Burnham ran unsuccessfully to become party leader in 2015, when he was beaten by Jeremy Corbyn.
He left parliament to become Greater Manchester mayor in 2017 but has remained an influential figure for some progressive groups within Labour, particularly those critical of Starmer's more centrist stance.
with PA
