Karie Murphy, the Unite-backed candidate, and Stephen Deans, the union's chairman in Scotland, were suspended last month as Labour leader Ed Miliband expressed his anger over claims that Unite sought to "stitch up" the selection process. Len McCluskey, the union's general secretary, strongly denied the claim.
At the time, Mr Miliband said his party had been "besmirched by the behaviour of a few individuals; that's why we suspended the local party; that's why we have now suspended two individuals".
On legal advice, the Labour leadership referred the matter to Police Scotland, but within days the force said there was not enough evidence to support a criminal investigation.
It is unclear if or when any Labour disciplinary hearings involving Ms Murphy and Mr Deans will take place.
When Unite was asked if Ms Murphy and Mr Deans should be reinstated, a spokeswoman said: "Yes. They should never have been suspended in the first place. They have done nothing wrong but still have this hanging over their heads."
She said that, with the party political conference season about to begin, Labour had to sort out the matter soon, saying: "The party can't continue to avoid the matter for much longer."
Labour's former campaign chief, Tom Watson MP, whom Ms Murphy works for as a parliamentary aide, said the reputations of Ms Murphy and Mr Deans had been "trashed" and added: "I'm sure when Ed looks at the detail, he'll see they are owed an apology."