Glasgow Govan MP Mohammed Sarwar took his seat in the Commons after the 1997 general election but was then charged with electoral fraud.
He was acquitted of the charges at the High Court at Edinburgh earlier this year and last night it was announced that he has been given the backing of all the branches of the party in his constituency.
The last one met last night and it has been decided not to open up a contest for the candidacy of the seat.
Mr Sarwar is expected to be the first Labour MP in Britain to be re-selected.
A Scottish Labour spokesman said party affiliates, such as trade unions, would have a say in the decision to re-select Mr Sarwar early next week.
The spokesman said: "Both Govan Labour party branches and affiliated organisations have input into this decision.
"Whether or not to open up the contest will be decided next week."
Neither Mr Sarwar nor his local party were allowed to comment on the situation, a spokesman for the Govan party said.Reuse content