A senior civil servant said that the shortlist had only been finalised in the past two weeks. The source added: "The sifting of applications has been done. The interviews will take place over the next couple of weeks."
The interview process will be led by CABE, but the panel also includes representatives from the Office of the Deputy Prime Minister and the Department for Culture, Media and Sport.
A CABE spokesperson said: "The final panel interviews will take place on 18 May. We are confident that we will be able to appoint someone before 31 May."
A source close to CABE said the appointment would only be delayed if contractual negotiations dragged on.
Two names linked to the job that are not believed to be on the shortlist are Chris Murray and Peter Redman.
Murray is CABE's head of education and training and was rumoured to have been interested in succeeding Rouse. However, it is understood that he did not apply for the role.
Former Notting Hill Housing Group chief executive Redman did apply. He quit registered social landlord Notting Hill last November following criticisms over its performance. Rouse spent three-and-a-half years at CABE. His new role at the Housing Corporation will give him control of a £1.2bn budget.