At a meeting of Labour's National Executive Committee, Jon Lansman proposed a motion to abolish the post of deputy leader, currently held by Tom Watson, citing his disloyalty over Brexit, according to two party officials.
The chair of the committee ruled the motion should be thrown out. Members voted 17 to 10 to overturn that decision but did not reach the two thirds majority required for it to pass, the officials said. The proposal is likely to go back on the committee's agenda on Saturday.
A party spokesman was not immediately able to comment. Watson's office did not immediately respond to a request for comment.
Corbyn will face pressure from delegates at the conference, which begins on Saturday in the English seaside town of Brighton, to shift towards openly backing remaining in the European Union.
Britain’s 2016 EU referendum has split not only British towns and villages but also parliament, with both Conservative and Labour leaders struggling to keep their parties united.
The divisions over Brexit were on display earlier this month when Watson said he supported pressing for a second referendum before an early national election.
His argument put him at odds with Corbyn, who says Labour would offer the people a second referendum on a credible option to leave against remaining in the EU, but only after an election.