The SNP fears losing the benefits that come with being the third party at Westminster if a Jeremy Corbyn victory prompts Labour to split.
The SNP currently holds the chairmanship of powerful Commons committees and has weekly questions to the Prime Minister, among other benefits.
But there are concerns over what would happen if a breakaway Labour group became the third largest in the Commons.
One SNP source said: “If Labour does split it would provoke some serious questions, especially if they become the third party.
"And there are worries that we might lose out".
Senior Labour figures will today meet to discuss fears that ‘entryists’, including Conservatives and those from the hard left, have infiltrated the party's leadership contest.
On the eve of the meeting one of Corbyn's rivals Andy Burnham called for unity as he issued a warning against Labour infighting.
"The longer this contest goes on, the more Labour risks turning inward and talking to ourselves," he said.
Last week another leadership contender Yvette Cooper became the latest in a string of senior party figures to warn of a potential split.
Labour appeared "to be polarising" between "different extremes", she warned.
Her ally Alan Johnson, the former Home Secretary and the MP many view as a potential leader of any rival Labour grouping, was forced to declare at the weekend that he was “going nowhere".
In a signal of how far advanced preparations had become, Mr Johnson also appealed to colleagues to stop "plotting and planning" a backbench rebellion against veteran left-winger Mr Corbyn.
Supporters were cautioned to keep "cool heads and steady hands".
"This is an election. If Jeremy Corbyn emerges as the winner I would counsel anyone thinking of splitting or separating to think again," he said.
Some within Labour fear that victory for Mr Corbyn will see the party repeat the struggles of the early 1980s and the circumstances which saw four senior party figures break away to form the Social Democratic Party (SDP) in protest at what they saw as a lurch to the left.
If enough Labour MPs split this time they could potentially replace the SNP, which currently has 56 MPs, as the third largest at Westminster.
After it secured 56 MPs in May the SNP demanded similar perks to those given to the Liberal Democrats when they were the third party in the Commons between 2005 and 2010.
These included the third party whip’s office, close to that of Labour and the Conservatives, and access the “usual channels”, which decide how parliamentary business is organised.
The thousands of pounds that the party receives in public 'short money', however, would not be affected by any Labour split as it is is based on a set calculations.
Mr Corbyn has rejected claims that his election could tear his party in two.
He said: “I don’t think there is any appetite for people to walk away from this and I look forward to the party working together."
In an apparent olive branch to critics, however, he said that he would appoint his shadow cabinet from a "very wide range of people" and that he hoped opponents will recognise the election result.
Mr Johnson has called on the Corbyn camp not to repeat the mistakes of the past.
"I certainly hope that Jeremy and his supporters, particularly the more finger-jabbing intolerant sections of them, are not going to try to repeat the 1980s," he said.
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