A senior figure in the organisation has faced criticism over her comments on social media and at an anti-Semitism training event.
Vice-chairwoman Jackie Walker, who has sparked criticism over comments made on social media and at an anti-Semitism training event, faces moves to unseat her from her post next week.
The leadership of the grassroots organisation set up by supporters of the Labour leader are due to meet on Monday.
A spokesman for Momentum said: "Members of Momentum's steering committee are seeking to remove Jackie Walker as vice-chair of the committee."
Ms Walker has faced calls to resign after leaked footage of the training event showed her saying she had not found a definition of anti-Semitism she could work with.
The video also showed her questioning why Holocaust Memorial Day was not more wide-ranging to include other genocides.
Ms Walker has previously suspended from the Labour Party for comments on social media saying Jews were the "chief financiers of the sugar and slave trade", but was readmitted after an investigation.
Trade union TSSA has threatened to remove its support of Momentum if Ms Walker remained in post.
Its general secretary Manuel Cortes said: "I am deeply saddened that a fellow member of our Labour and trade union family holds such anti-Semitic views."
In an interview with Channel 4 News, when asked whether she had considered stepping down amid critivism from some Jewish groups, Ms Walker said: "Some other prominent Jewish groups, of which I'm a member of, think a very different thing.
"What we have to look at when we're talking about this subject, particularly at the moment, is the political differences that are underlying this as well."
Whoever leaked the footage from the training event "had malicious intent in their mind", she said.
She also said she was anti-Zionist rather than anti-Semitic, adding: "I think Zionism is a political ideology, and like any political ideology, some people will be supportive and some people won't be supportive of it. That's a very different thing."
Dogged by accusations of anti-Semitism in Labour's ranks, Mr Corbyn used his recent conference speech to denounce it as an "evil".
He also pledged to fight against "prejudice and hatred of Jewish people".
A review into racism in Labour, led by former Liberty director Shami Chakrabarti, found the party was "not overrun by anti-Semitism, Islamophobia or other forms of racism".
But the report was criticised by Jewish leaders and MPs, who argued its credibility was undermined because Ms Chakrabarti was nominated for a peerage by Mr Corbyn just weeks after its publication.