Darren Hughes has not yet formally resigned from Parliament but the Labour Party says he has indicated he will do so by next Tuesday.
The list MP announced he was resigning last Friday, just days after it was revealed police are investigating a sex complaint made against him by an 18-year-old man.
He insists he has done nothing wrong and is cooperating with the police inquiry.
To resign, Mr Hughes has to write to Parliament's Speaker, but Lockwood Smith's office says it has not recieved a letter so far.
Once Mr Hughes has resigned, the Electoral Commission will then contact the next person on the Labour Party list, Judith Tizard, about taking his place.
Labour has indicated it would prefer the former minister and the next four people on its list did not return to Parliament, to allow former MP Louisa Wall to take up Mr Hughes' seat in the House.