Sinn Fein group leader group leader Councillor Sandra Duffy says they will table the motion if Alderman Derry Hussey does not step down over his drink-driving record.
The deputy mayor has three previous convictions for drink drinking.
The family of local man Martin Gallagher, who was knocked down by a drink driver in 2009, have called on Cllr Hussey to quit as deputy mayor.
Said Cllr Duffy: “Sinn Fein has already objected to Derek Hussey’s appointment as chairman of the Policing Community Safety Partnership (PCSP) on the grounds that someone with repeated drink-driving convictions should not be leading a body tasked with public safety matters,” she said.
“While we accept that everyone is entitled to a second chance, it is clear that Derek Hussey has had several but continued to display the most atrocious disregard for public safety.
“This has compounded the trauma of local families bereaved by drink drivers, who have long campaigned for a zero-tolerance approach to drink driving.
“In light of this, we feel it is inappropriate for Mr Hussey to continue in his current position.
“He does not enjoy the confidence of the wider public and is undermining the approach which all public bodies must take to issues such as drink driving which are an ongoing and extremely serious issue in this society.
“Therefore, Sinn Fein will table a motion of no confidence in him at Thursday’s full council meeting, if he continues to refuse to listen to the concerns that have been raised.
“We are conscious that, even if passed, such a motion does not compel him to resign – however, it would demonstrate the strength of feeling on this issue and certainly add to the moral pressure on Mr Hussey and his party.”
SDLP councillor Brian Tierney has also called on Alderman Hussey to reconsider his position as deputy mayor.