DUP deputy leader Peter Robinson may soon be giving up his council seat in Castlereagh.
Peter Robinson may give up his council seat
The party is currently reviewing potential conflicts of interest between senior members of the assembly who are also councillors.
A DUP spokesman said about half a dozen members are affected.
They include Mr Robinson, the new finance minister, and the new environment minister, Arlene Foster, who also sits on Fermanagh council.
Party leader Ian Paisley will be sworn in as first minister of a new Northern Ireland power-sharing assembly on 8 May, with Sinn Fein's Martin McGuinness as deputy first minister.
In the previous assembly both Mark Durkan, the SDLP finance minister, and the UUP environment minister, Sam Foster, resigned their council posts.