Edinburgh South MP Ian Murray could face an attempt to de-select him as the Scottish Labour candidate before the next general election.
The Unite union is reportedly pushing to remove him as the party's candidate in any forthcoming election.
A vote is due to take place in his local Labour party on Thursday evening, the BBC reports.
Murray was Labour's only MP north of the border between 2015 and 2017 and was returned with an increased majority of 15,514 votes at the last general election.
He released a statement in response to the issue on Tuesday evening, saying "I’ve only ever put my communities and constituents first."
Party rules mean a contest to replace a sitting MP can be triggered if a third of members or affiliated unions supports it.
He said: "It is disappointing that in the week where I'm leading the People's Vote campaign in Scotland and working around the clock to maintain the cross party coalition that's defeating Boris Johnson's disastrous Brexit in order to protect workers' jobs and rights, that this is Unite's priority.
"My constituents are my priority and I won't be distracted from fighting for them."
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